Carmen D’Amico contributed a proto-version of the Tent Vanish in his “Toss Over Card” routine to The Tarbell Course in Magic, Lesson 60, 1948, p. 86 (where he is credited as “Carmen Damico”). In it, the card to be vanished is held at the tips of the left fingers, in an elevated position over the deck, parallel with the cards beneath. When the right hand comes over the card, apparently to palm it away, the card is secretly dropped onto the deck. The general method is that of the Tent Vanish, but with the card is held parallel with the deck rather than obliquely over it.
The now-standard handling of the vanish, with its card angled up on one side, was explained in Dai Vernon's “Slow Motion Four-Aces” routine from Stars of Magic, Series 6 No. 2, 1950 (p. 90 of the 1961 compilation book). This handling is more complex than that of the now-common Tent Vanish, because the card that will disappear is held face outward above the face-down deck. The right hand, which palms several face-down cards, secretly drops them onto the face-up card while pretending to palm it. The same technique was published as “Dai Vernon’s French Drop Colour Change” in Dai Vernon's Inner Secrets of Card Magic, written by Lewis Ganson, 1959, p. 52. This vanish was later attributed to Arthur Finley, a friend of Vernon from New York’s inner circle. Jacob Daley called it “Findley’s [sic] Book Color Change” in his personal notebooks (Vol. 3, p. 61) from the 1930s and ’40s; see Jacob Daley’s Notebooks, n.d. (c. 1972), Item 707, n.p. An earlier excerpt of this move from the notebooks appeared in The Pallbearers Review, Vol. 7 No. 2, Dec. 1971, p. 472. (Daley and Vernon misclassified it as a “color change” apparently because of the similar overt actions made by the hands when doing both sleights.)
The simplified Tent Vanish, in which a single back-outward card is let to fall secretly onto the deck, is claimed by both Larry Jennings and Bruce Cervon. It appears within the “Jennings’ Open Travellers” routine in Alton Sharpe’s Expert Card Mysteries, 1969, p. 41, which also appears to be where the name “Tent Vanish” was coined. Jennings’s name was more explicitly attached to the technique by J. K. Hartman in Packet Magic, 1972, p. 28, where the move is taught in “Tripsters” and called “the Jennings variation of Dai Vernon’s Tent Vanish.” However, Bruce Cervon claimed to have used the technique (which he calls the “Bluff Tent Vanish”) since 1966. He makes this claim in his March 14, 1998 private email correspondence detailing his side of the "Face Up Flyers" / "Open Travellers" debate. Regardless of who developed this simplified handling, it brought the Tent Vanish full circle, landing remarkably close to what D’Amico had published two decades earlier.
Many magicians have since returned to Vernon's original face-outward orientation and have developed new means to achieve it. Among these are Anthony Owen’s Caravan Move from The Dungeon, No. 4, Jun. 1994, p. 43; Kevin Kelly’s A Face Up Tent Vanish in Pasteboard Odyssey, 1997, p. 5; Jay Sankey’s Pup Tent Vanish on Sankey Very Much video, 1998, 5:53; Jack Parker’s Face Up Tent Vanish in MAGIC magazine, Vol. 13 No. 5, Jan. 2004, p. 78; and Ken Krenzel’s Striking the Tent in Relaxed Impossibilities, 2009, p. 103.