The phrase to do a vanishing act (or trick), also to do a disappearing act (or trick), means: to disappear suddenly without leaving information about one’s whereabouts.

This is a metaphor from conjuring, in which the noun vanishing act (or trick), also disappearing act (or trick), designates:
– an act of making a person or thing disappear as if by magic;
– an act of disappearing in this manner.

The earliest literal uses of the noun vanishing act (or trick), also disappearing act (or trick), that I have found are as follows, in chronological order:

1-: From a review of the attractions at Franconi’s Cirque de Paris, in Cremorne Gardens, London, published in the Morning Advertiser (London, England) of Monday 14^th July 1851 [No. 18,736, page 6, column 4]:

M. Courteau, the clown, by his pantomimic expression, his agility, and, above all, his vanishing trick, when almost in the clutches of the French police, by aid of the “enchanted goblet,” was a wonder.

2-: From a review of an entertainment titled The Great Wizard of the North, performed by Professor Anderson at the Rotundo, Dublin, published in Saunders’s News-Letter and Daily Advertiser (Dublin, County Dublin, Ireland) of Tuesday 16^th September 1856 [No. 35,692, page 2, column 5]:

Professor Anderson is assisted by a very fine little boy, a mere child in years, but exceedingly handsome, and evidently chosen for his intelligence. He figures in the opening scene, known as the “Cataleptic Couch,” in which apparently under the influence of mesmerism, his little frame is put into varied and seemingly impossible posture [sic]; and subsequently, in the miniature dress of a Guardsmans [sic], he catches in his mouth a marked bullet fired from a fusil de salon. The little fellow afterwards in the costume of a sailor is taken with his sister, and [sic] a portmanteau of the largest size from a scrap-book but six inches in thickness; and at the close assists in the now well-known disappearing trick.

3-: From Public Amusements, published in Lloyd’s Weekly Newspaper (London, England) of Sunday 2^nd June 1861 [No. 967, page 8, column 3]:

The fortunes of Astley’s Amphitheatre have undergone a complete change. […] But the circus remains, and if the equestrian performances therein be not on so lavish a scale as of old, it is because some novelties demanded by the age are introduced in their place. […] Interspersed throughout the evening, are the quaint drolleries of Harry Croneste, the most diverting of modern clowns. His vanishing trick, and subsequent appearance in a private box, is managed very neatly.

The earliest figurative uses of the noun vanishing act (or trick), also disappearing act (or trick), that I have found are as follows, in chronological order:

1-: From the following advertisement, published in The New York Herald (New York City, New York, USA) of Thursday 22^nd April 1869 [No. 11,933, page 11, column 6]:

THE EVENING TELEGRAM.
POLITICAL LEGERDEMAIN.
For an expose of the tricks and traps of
LOCAL PRESTIDIGITATEURS
SEE THE EVENING TELEGRAM OF SATURDAY NEXT.
All the games and deceptions of the magician exposed.
THE RING TRICK SHOWN UP,
And the modus operandi of the performer made plain to the spectator. Also the
GREAT VANISHING TRICK.
SEE SATURDAY’S TELEGRAM CARTOON.

2-: From the Montrose Standard, and Angus and Mearns Register (Montrose, Angus, Scotland) of Friday 27^th January 1871 [Vol. 35, No. 1,753, page 5, column 5]:

ABERDEEN.

A New Ghost Story.—It would seem either that our good city is not entirely free from supernatural visitation or that superstition lingers in the mind of the community to a large extent. For a few nights back quite a commotion has been created in the north-eastern district of the town by the reported appearance of a ghost in a house in the Causewayend locality, and the place has been visited on some evenings by about a thousand persons eager for a sight of the stranger. So far as can be gathered the facts of the case are that one of the inmates of the house—a young woman—stated several days ago that her bedroom had been invaded during the night by a lady dressed in the orthodox ghostly colour of apparel, and that the intruder so far forgot all lady-like manners as to remove the bed clothes from above the sleeper. This caused the young woman to jump to the floor, and make the dreadful discovery of the unearthly character of her visitor, for on being followed the figure disappeared through the keyhole or vanished into thin air. A man is also stated to have obtained a sight of the unwelcome guest. She appeared to him to be attired in silk—of what hue is not mentioned—and so little impressed was he at first with the idea that there was anything out of the common that he pursued the lady into closet and pantry till the vanishing trick was repeated.

3-: From Greenpoint News, published in The Brooklyn Daily Times (Brooklyn, New York, USA) of Saturday 29^th June 1878 [page 4, column 7]—here, what the noun disappearing act refers to is obscure:

The Presbyterian Sunday School of Greenpoint, went on its annual excursion and picnic to Oriental Grove, Thursday. About nine o’clock the barge Anna, accompanied by a tug-boat, left the foot of Noble street, packed with as merry a crowd of pleasure seekers as ever went from the ’Point on a similar expedition. The grove was reached in about two hours and a quarter. As soon as all were ashore the school took up its line of march for the grove. The “disappearing act” followed and in a few minutes the commissary department * became a total wreck. Then, swinging, base ball playing, croquet playing, and many other means of amusement were indulged in until about five o’clock, when the barge with her load of 1,200 people moved slowly down the river. The boy band from the Soldiers and Sailors’ Home, played a well selected list of popular airs. At seven o’clock, the Anna with her consort and with flags fluttering and band playing landed at her wharf foot of Noble street.

* The noun commissary department designates a branch or department of the armed forces responsible for the supply of food and other provisions to troops.

4-: From The Rooks County Record (Stockton, Kansas, USA) of Saturday 14^th August 1880 [Vol. 1, No. 37, page 3, column 3]:

—A bad preacher of Logansport, Indiana skipped out with all his wife’s money, came to Leavenworth, Kansas, married a young lady there and repeated the disappearing act again. Nobody knows his whereabouts. Satan will smile when he gets his clutches on him.

5-: From a review of The Belle’s Stratagem, a comedy by the British playwright Hannah Cowley (1743-1809), produced at the Lyceum Theatre, London—review published in The Era (London, England) of Saturday 23^rd April 1881 [Vol. 43, No. 2,222, page 14, column 1]:

The comedy is presented in its compressed form, in three acts […]. Admirers of the comedy, as it stood, will be likely to object to the liberties that have been taken; to the improvement out of existence, so far as the Lyceum stage is concerned, of some old friends and some good scenes; and to the vanishing trick by which not a few of the good things of the original text have been got rid of.

6-: From The Greenville Daily News (Greenville, South Carolina, USA) of Saturday 15^th October 1881 [page 2, column 2]:

The Columbia Register will please consider itself patted on the back with the enthusiastic approval of The Daily News, for its emphatic repudiation of desire for Joseph E. Brown and Hr Kimball in South Carolina. We prefer a little less sound, fury and enterprise, and a little more of good, old-fashioned articles known as Honesty and Truth. We had better be poor and slow than dubious and rapid. We had quite a number of Kimballs, Browns and Bullocks at one period in our career, but they executed a grand vanishing act amid the tremendous applause of our entire population. The aspects of sundry of our sheriffs, and the color of the popular shirt failed to harmonize with their feelings. They have exhibited a progressiveness in the direction of the setting sun that was prudent and commendable.

7-: From The Chattanooga Daily Times (Chattanooga, Tennessee, USA) of Wednesday 24^th May 1882 [page 1, column 4]:

SENATOR DON CAMERON.
Republican “Boss” of Pennsylvania.

The last few years have seen the fall, or decadence, of power of many a Republican “Boss.” […] Only Don Cameron, of Pennsylvania, holds undisputed sway and has never suffered a defeat.
James Donald Cameron, the subject of our sketch, was born in Middletown, Pa., in 1833, graduated at Princeton College, and began life as clerk in the Middleton [sic] bank, where he rose to the position of cashier. He failed to acquire all the modern accomplishments, and never performed the great embezzling or disappearing act for instance, but still he was counted a good cashier.

8-: From an account of the voyage of the New-South-Wales Rugby-Union team to New Zealand, on board the New-Zealand ship Rotomahana, on Thursday 30^th August 1882—account by U. Donohue, published in The Sydney Mail (Sydney, New South Wales, Australia) of Saturday 4^th November 1882 [Vol. 34, No. 1,165, page 804, column 1]:

At 6 o’clock the dinner-bell rang, and the passengers collected in the saloon […]. Only a few minutes were allowed for the fellow-travellers of the next few days to stare at each other and take stock, and then a small army of stewards invaded the saloon, whipped off the dishcovers with a clatter, and disappeared again. Having satisfactorily performed the disappearing trick, they returned and speedily supplied the plates of the hungry with the meats of their choice.

9-: From the Buffalo Morning Express (Buffalo, New York, USA) of Friday 26^th December 1884 [page 4, column 3]:

The case of William B. Jenkins, the Rochester insurance agent who “mysteriously disappeared” in New-York a few weeks ago, is detailed in our special despatches this morning. Briefer mention was made last week. Rochester had an epidemic of disappearances a year ago, but the victims did not go from home to do their vanishing act. There are so many guesses admissible in the Jenkins case that it is hazardous to venture upon any particular one. A German thinker’s theory of “cosmic holes,” lately set forth in the New-York Times, comes to mind. The German supposes—or a Times young man does for him—the crust of the universe to abound in weak spots, upon which if a mortal steps he vanishes from mortal view forever, not dying, not yet living, simply held in a vacuum, something like “Blest Nirvana, sinless, stirless rest, the change that never changes,” only the cosmic holes are not to be aspired to, and may snap up the ungodly as well as the incipient Buddh [sic]. To come down to more easily understood things, Mr. Jenkins may be found in the morgue, the hospital, the asylum, or he may not be found at all.

10-: From Christmas Games, by ‘Angelica Kaufdrop’, published in The Sporting Times (London, England) of Saturday 27^th December 1884 [No. 1,110, page 2, column 2]:

The Two Quid Trick.

This has the merit of simplicity. Say that you are going to do a vanishing trick, and borrow two sovereigns off the company, and then slip quietly out and go down to the Raleigh Club. This is a very old trick, but always popular. I know—indeed, I do know—I know that what I say is right.

11-: From The Daily Nebraska State Journal (Lincoln, Nebraska, USA) of Friday 28^th August 1885 [16^th Year, No. 29, page 7, column 3]:

“THIS LIFE’S A DREAM.”
A California Romance at Large.

A curiosity was received by John Schmittel yesterday in the shape of one of a box of California pears, which bore upon one side the words “This life’s a dream.” The words had evidently been cut into the pear when it was green and considerably smaller than at present, as the fruit had grown out beyond the part the growth of which was retarded by the cutting. The pear has connected with it doubtless a whole romance of moonlight walks and tender sighs and pleading love and cruel rejection. Some California swain has sat beneath the pear tree in the soft, subdued starlight—a pear tree affords plenty of shade from the starlight—and poured out into heedless ears a passionate tale of devotion, while the dewdrops sparkled on the velvety grass and the melody making mule threw the spell of his soft, weird song over the tender scene; and when the tale was told and the cruel maid had told him that she had loved him simply as a brother, and only a half-brother at that, and had done the disappearing act with the mocking-laugh attachment, he has shinned up the tree and eased off his agony on the pear and then probably gone off on a two weeks’ toot. If the tender memories connected with the pear make it of any value to him, he can have it by applying to John Schmittle [sic] and paying the cost of this rhapsody.