The phrase tarpaulin muster designates the collecting of a pool of money, to be used either to provide assistance to some (other) person(s) or cause, or to buy drinks for the contributors.

The U.S. author and columnist Robert C. Ruark (1915-1965) used this phrase figuratively in Aswan Dam Earns Enemies for U.S., published in The Eau Claire Leader (Eau Claire, Wisconsin, USA) of Sunday 23^rd November 1958 [Vol. 77, No. 277, page 4, column 1]:

Perhaps you could call me a man of testy temper, but I boiled slightly over the grounds when Dr. Charles Malik, president of the United Nations General Assembly—and former foreign minister of Lebanon—calmly suggested the other day that the United States pull a tarpaulin muster and dig up enough dough to give the proposed Aswan Dam project to the Egyptians as a gift.

Although tarpaulin muster was used by “six poor clerks” in the text containing the earliest occurrence that I found (cf., below, quotation 1), this phrase originated among seamen: such funds were originally collected by having the ship’s crew drop their money onto a tarpaulin (i.e., a sheet of waterproof canvas).

George Harrison mentioned that practice in the column Over the Mersey Wall, entitled that day So the ship held a tarpaulin muster, published in the Liverpool Echo and Evening Express (Liverpool, Lancashire, England) of Wednesday 17^th October 1962 [No. 25,771, page 2, column 3]:

It was when his ship, the m.v. Santander, was nearing Peru that the first cablegram arrived, for Able Seaman George Halliwell, whose home is at 18 Frith Street, Kirkdale, Liverpool 20.
The cable told him that his wife […] was seriously ill in hospital. […]
George Halliwell, on his A.B.’s pay, […] hadn’t anything like the £200 which it would need for the air fare back to England from Lima, Peru.
[…]
The story of George Halliwell’s distress came to Captain Pepper’s ears. Without a word to George, the captain arranged a “tarpaulin muster” to raise the money to fly him home.
For non-seagoers, a “tarpaulin muster” is a sheet into which everybody throws the money he can afford for the cause that is at stake—and it is always a good cause and a good stake.

The earliest occurrences of the phrase tarpaulin muster that I have found are as follows, in chronological order:

1-: From the Monthly Record of the Five Points House of Industry (New York City, New York, USA) of January 1863 [Vol. 6, No. 9, page 198]:

The responses to the Thanksgiving appeal were so kind and hearty, and show so thoroughly the public interest in our work, we can not refrain from noticing them somewhat at large, confident that other hearts will feel as ours have in dwelling upon them.
[…]
“Inclosed sixty cents, being a tarpaulin muster by six poor clerks for the relief of the little children at the Five Points.
“Yours respectfully, CICERO.”

2-: From Local Intelligence, published in The Daily Morning Chronicle (San Francisco, California, USA) of Sunday 17^th January 1869 [Vol. 9, No. 2, page 3, column 1]:

Generous Contribution.—We suggested, a few days ago, that money should be raised by voluntary contributions for the benefit of those small-pox patients who, while convalescent, require assistance. We received yesterday, in response to the suggestion, the following note:
Editors Morning Chronicle: Please hand to the San Francisco Benevolent Society the accompanying $35, the result of a “tarpaulin muster” made by some of the boarders of the “Sailor’s Home” in aid of “suffering convalescents” from small pox, suggested by an article in the Chronicle last week on the subject. May others go and do likewise. Yours, JACK.
The note was accompanied by the coin. We have seen the Secretary of the San Francisco Benevolent Society, and he informs us that he will appropriate the money in accordance with the designs of the contributors. We are glad that the Chronicle has effected a commencement of the good work, and “Jack” is certainly entitled to great credit for taking the initiative by a generous contribution.

3-: From one of the miscellaneous news-items from Mianus (Connecticut), published in The Port Chester Journal and Westchester County Advertiser (Port Chester, New York, USA) of Thursday 2^nd March 1871 [Vol. 3, No. 119, page 2, column 6]—bbl. is the abbreviation of barrel, used as a measure of capacity:

“Tarpaulin muster” is played out at Smith’s, the boys having drank up this Winter the six bbls of cider.

4-: From a letter to the Editors, dated 29^th April 1871, by ‘J. P. R.’, denouncing “the reckless, wholesale granting of licenses to brewers and spirit merchants” in Liverpool, published in The Liverpool Mercury, and Lancashire, Cheshire, and General Advertiser (Liverpool, Lancashire, England) of Tuesday 2^nd May 1871 [No. 7,261, page 7, column 7]:

The system of over-measure, I contend, is the chief cause of drunkenness among females and what has caused the ruin of many a good woman. It happens thus—A meets B, C, and D, and, after exchanging the compliments of the day, proposes to “go and have a glass of ale together.” They accordingly make for one of the brewer’s houses, call for “a pint of ale in a jug,” and deposit 2½d. on the counter. They are served with fully one quart imperial measure. Next B, who, perhaps, is a modest young woman, and having only just come to reside in the neighbourhood, and not wishing to appear less than her neighbour, or perhaps run the risk of being called a stingy or skinny so-and-so, calls for the next pint, and so forth, until a regular club is established among them, and at length so great is the temptation that when one is unable to raise the requisite fund, a what is termed tarpaulin muster is got up for the purpose. When this nefarious system of over measure is put down, then, and not till then, will drunkenness begin to decrease.

5-: From The Daily Southern Cross (Auckland, Auckland Region, New Zealand) of Saturday 23^rd August 1873 [Vol. 29, No. 4,992, page 2, column 6]:

Our Cambridge correspondent, writing on the 20^th August, says:—Mr. James Mackay returned a few days since from his second Taupo trip, and has, I believe, succeeded in finding a good line for the railway from here to that place […]. Mr. Mackay’s negotiations are carried on now with the Ngatirakawa only, who will have a deal to say relative to the Taupo railway. This tribe intend to hold a large meeting shortly. The Government, I think, are trying to strengthen their hands by sending over the Wellington portion of the tribe, who arrived at Te Waotu last week, bringing in their pockets subscription lists for native parsons, good moral tracts, and such like remedies for the present state of darkness (mental) in which their Waotu brethren are living; but I am afraid a “tarpaulin muster” for a bottle of grog would find more favour amongst them than dubbing up for the purpose of keeping another native preacher.