The noun pumpkinification was coined after Hellenistic Greek ἀποκολοκύντωσις (Latin ăpŏcŏlŏcyntōsis), which:
– means transformation into a pumpkin;
– is the title of a travesty ascribed to Seneca [1], according to which the deceased Roman emperor Claudius [2], instead of being elevated to divine status, is changed into a pumpkin.

Modelled on Hellenistic Greek ἀποθέωσις (Latin ăpŏthĕōsis), meaning elevation to divine status, ἀποκολοκύντωσις is composed of:
– the prefix ἀπο- (= apo-);
– κολοκύνθη (Latin cŏlŏcynthis), meaning pumpkin;
– the suffix -ωσις (= -osis).

The English lexicographer William Smith (1813–1893) gave the following explanations, s.v. Seneca, in Dictionary of Greek and Roman Biography and Mythology (London: Taylor, Walton, and Maberly, 1849):

Apocolocyntosis, is a satire against the emperor Claudius. The word is a play on the term Apotheosis or deification, and is equivalent in meaning to Pumpkinification, or the reception of Claudius among the pumpkins. The subject was well enough, but the treatment has no great merit; and Seneca probably had no other object than to gratify his spite against the emperor. If such a work was published in the lifetime of Seneca, he must have well known that it would not displease either Agrippina or Nero; and it leads to the probable inference, that the poisoning of Claudius was not a matter which he would complain of. In fact, the manner of the death of Claudius was a subject for the wits of the day to sport with.

The following additional details are from Corsica: picturesque, historical and social: with a sketch of the early life of Napoleon, and an account of the Bonaparte, Paoli, Pozzo Di Borgo, and other principal families (Philadelphia: John E. Potter and Company, 1855), the translation by the U.S. politician Edward Joy Morris (1815–1881) of Corsica (1854), by the German historian Ferdinand Gregorovius (1821–1891):

As Seneca had been banished in the first year of the reign of Claudius, and had returned in the eighth of his government, he was enabled to enjoy himself under “this divinity and heavenly star.” But Claudius died one day, because Agrippina had mixed some poison in the pumpkin which served him for a drinking vessel: the potion had been prepared by the famous Locusta. The death of Claudius afforded Seneca the long-desired opportunity of giving vent to his revengeful feelings. He made him fearfully pay for his sufferings in exile, in his satire on the deceased monarch, entitled Apokolokyntosis—a pamphlet of astonishing wit, and almost incredible boldness, which is fully comparable in geniality to the writings of Lucian himself. The title is an amusing parody of the idea of the translation, or apotheosis of Claudius among the gods, and he calls it rather the Pumpkinification, or, reception of Claudius among the pumpkins, because he was poisoned with a pumpkin.

Another translator of Ferdinand Gregorovius’s Corsica, Russell Martineau (1831–1898), used gourdification instead of pumpkinification in Corsica in its picturesque, social, and historical aspects: the record of a tour in the summer of 1852 (London: Longman, Brown, Green, and Longmans, 1855):

As Seneca was banished to Corsica in the first year of Claudius, and returned in his eighth, he could rejoice in “this deity and this celestial star” for more than five years longer. But Claudius died suddenly, Agrippina having given him poison mixed by the notorious Locusta, in a gourd that served as drinking-vessel. The death of Claudius brought Seneca the longed-for opportunity of giving vent to his vengeance. He took terrible reprisals for his banishment, by writing upon the deceased the Apocolocyntosis, a pamphlet of astonishing wit and incredible audacity, fully equal in genius to Lucian. The very title is an invention of genius; it parodies the notion of the apotheosis or translation of the Emperors to the gods, and signifies the translation into the society of gourds, or gourdification of Claudius, who was poisoned by a gourd. This satire is well worth reading.

The noun pumpkinification has come to mean extravagant or absurdly uncritical glorification. The earliest occurrence that I have found is from Apocolocyntosis, published in The Saturday Review of Politics, Literature, Science, and Art (London, England) of 6^th December 1884—this text also contains the nouns pumpkinifier, denoting a person who extravagantly or absurdly glorifies another, and pumpkinity, denoting the characteristics of extravagant or absurdly uncritical glorification:

For the present we have to do with apocolocyntosis; and it must be a very unreasonable reader who will not admit that apocolocyntosis is a mouthful and a handful quite enough to occupy one reviewer at one time.
Long before this the well-regulated journalist who has his books of reference in proper order will have run to them to see what apocolocyntosis means. His dictionary will refer him to Seneca, and Seneca will suggest the invaluable Dr. William Smith. Here, however, we proceed to cut the ground from under the well-regulated journalist’s feet pro nostra malevolentia [3]. He had a lightning sarcasm ready—or, rather, Dr. Smith had one ready for him. Of the Apocolocyntosis, or Pumpkinification of Claudius, Dr. Smith writes that “the subject was well enough, but the treatment has no great merit, and Seneca probably had no other object than to gratify his spite against the Emperor.” Now, independently of the fact that our treatment is, of course, worthy of any subject, and that we have no spite against Mr. Gladstone [4] or anybody else, this citation of ours has completely stolen the ingenious journalist’s thunder. He cannot make the joke against us, for we have made it against ourselves. But, putting this aside, let us get to our pumpkins. There appeared in the Pall Mall Gazette of Monday an article entitled “Apotheosis,” which must surely have suggested Seneca’s skit to any one who was aware of its existence. We know that to some delicate ears it will sound shocking to conjoin the ideas of Mr. Gladstone and a pumpkin. But the resemblance is really too obvious. Not even the P. M. G. itself, or the Spectator, or Sir William Harcourt [5], will deny that Mr. Gladstone is “some pumpkins” of a politician. Others may have been struck with the admirable and suggestive spectacle, just now frequent at the fruiterers, of a redistributed pumpkin intoxicated with the exuberance of its own pulposity. His party, too, to adopt the adorable Miss Neverout’s phrase [6], love Mr. Gladstone “like pie”—like pumpkin-pie. The pumpkin is the largest of fruits, and Mr. Gladstone is the greatest of statesmen. It is clear that pumpkin is etymologically the diminutive of pump [7], and the flow of Mr. Gladstone’s eloquence has frequently reminded admirers and others of the useful engine from which Pump Court [8] derives its name. But there is no need to continue, and to tell the truth, the resemblance is even more suggested by the style of the eulogist than by the characteristics of the eulogized. We feel much more inclined, we own, to vote for Mr. Gladstone’s apocolocyntosis than for his apotheosis. But if anything could make a pumpkinification out of a deification, it would certainly be the style of the P. M. G. article of Monday last.
The fact that Mr. Gladstone could not get his Reform Bills through without taking Lord Salisbury [9] into partnership is, it seems, “the last and crowning tribute which will be paid to the personal ascendency of our great leader.” “How great Mr. Gladstone is we shall never really know until he is gone. At present he is not so much appreciated as idolized. No man ever had so deep, so powerful a hold upon the imagination of the people as the Prime Minister has to-day. When he travels about the country his journeys are more than royal processions. Crowds wait at every railway-station to clamour for a passing word, and a hundred newspapers give precedence to reports of his wayside talk over news of the fall of Ministries or the fate of campaigns. In the popular imagination he has undergone an apotheosis not unlike that which in the mind of the Russian peasant takes place on the coronation of the Czar.” And then we are told that “this revival of the old kingship is the first-fruits of English democracy,” and that “it is well that the first monarch of the new line should bear a character so lofty as that of Mr. Gladstone.” “Absolute,” “the Lancelot of our time” (has Mr. Gladstone been falling in love with somebody else’s wife? [10]), “marvellous energy,” “supernatural versatility,” “a political career which has added lustre to the annals of England,” “South Africa tranquil under the British ægis” (with a picture of Majuba Hill [11] instead of the Gorgon’s head, we suppose), are a few more of the phrases whereby the pumpkinifier constructs his pumpkin; and he winds up by observing, that if Mr. Gladstone will only make the navy bigger, he may retire “with the proud consciousness that he has restored England to something like that position of security,” abroad and at home, “that she enjoyed before the malign influence of Lord Beaconsfield [12] cast its evil shadow on the land.” Which last phrase, by the way, from a periodical which has cribbed Jingoism whole, merely substituting Radicalism for Toryism in domestic politics, is, to say the least, ungrateful. Also the restoration of England to the proud position in which she was when Russia tore up the Treaty of Paris and flung the fragments in her face would, we might have thought, have scant charms even for a Radical Imperialist. But one does not expect knowledge of history—even of history a dozen years old—from Radicals; and we certainly do not mean to enter into a serious discussion with the Pall Mall Gazette on the foreign policy of Mr. Gladstone. The fun of the pumpkinification is, in the first place, the true pumpkinity of its style, and, in the second place, the admirable logic of its argument. The docile mind receives the statements respecting Mr. Gladstone’s godlike character and reputation, and only mildly asks for evidence. The evidence is forthcoming. “Crowds wait at every railway station to clamour for a passing word and a hundred newspapers, &c. &c.” Mr. Gladstone is all the P. M. G.’s fancy could paint a perfect statesman; he’s lovely, he’s divine, for precisely the same reason which would in the days of travelling mountebanks have established the divinity of Dr. Paracelsus [13] or Dr. Agrippa [14]. Vera incessu patet colocyntha [15]: you may know the true pumpkin by his progresses and the gapers thereat.

Notes:
1 Lucius Annaeus Seneca (circa 4 BC–AD 65) was a Roman statesman, philosopher and playwright. In 49, he became tutor to Nero (Nero Claudius Caesar Augustus Germanicus – AD 37–68), emperor from 54 to 68.
2 Claudius (Tiberius Claudius Drusus Nero Germanicus – 10 BC–AD 54) was emperor from 41 to 54. His fourth wife, Agrippina, is said to have poisoned him.
3 The Latin pro nostra malevolentia means for our own malevolence.
4 William Ewart Gladstone (1809–98) was the Prime Minister of the United Kingdom from 1868 to 1874, from 1880 to 1885, in 1886, and from 1892 to 1894.
5 William Harcourt (1827–1904) was then the Home Secretary.
6 This refers to A Complete Collection of Genteel and Ingenious Conversation, according to the Most Polite Mode and Method now used at Court, and in the Best Companies of England (London: Printed for B. Motte, and C. Bathurst, 1738), by the Irish satirist, poet and Anglican cleric Jonathan Swift (1667-1745). In this book, Miss Notable says: “I own, I love Mr. Neverout, as the Devil loves Holy Water; I love him like Pye, I’d rather the Devil had him than I.”
7 In fact, the noun pumpkin is an alteration of pumpion, variant of pompion, with remodelling after words ending with the diminutive suffix -kin.
8 Pump Court, Temple, London, was so called from the pump in its centre.
9 Robert Gascoyne-Cecil (1830–1903), 3^rd Marquess of Salisbury, was then the Leader of the Opposition.
10 In Arthurian legend, Lancelot, the most famous of Arthur’s knights, was the lover of Queen Guinevere.
11 This refers to the Battle of Majuba Hill (27^th February 1881), the final and decisive battle of the First Boer War.
12 Benjamin Disraeli (1804–1881), 1^st Earl of Beaconsfield, was the Prime Minister of the United Kingdom in 1868 and from 1874 to 1880.
13 Paracelsus (Theophrastus Phillipus Aureolus Bombastus von Hohenheim – circa 1493–1541) was a Swiss physician.
14 Heinrich Cornelius Agrippa von Nettesheim (1486–1535) was a German physician, expert on occultism, and philosopher.
15 This is a humorous variant of what the Roman poet Virgil (Publius Vergilius Maro – 70–19 BC) said of the goddess of beauty: Et vera incessu patet Dea, Her step betrays the goddess.