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This principle was used as far back as the 17th century, appearing in two anonymous, unpublished manuscripts: Sloane 424, c. 1600s, p. 160 of the Pieper translation; and the Asti Manuscript, c. 1700, p. 58. These manuscripts were translated in Gibecière, Vol. 5 No. 2, Summer 2010, p. 141-172, and Gibecière, Vol. 8 No. 1, Winter 2013, p. 29-234, respectively. These methods didn't use a rubber band; instead, they used a card folded in half, and a finger or thumb across the pack to cover the seam.
The idea didn't hit the printed page until the mid-nineteenth century. It appeared with a half-card in the trick “Hold it Fast” in anonymously authored Parlour Magic, 1838, p. 157. Later, it was included in R.P's Ein Spiel Karten, 1853, p. 22 of the Pieper translation.
During the latter half of the 19th century, the idea was applied to slate writing. (See, for example, “The Interrupted Flap” in William Robinson's Spirit Slate Writing and Kindred Phenomena, 1898, p.47.)
The principle, once again applied to paper, was rediscovered in the twentieth century, and has stuck ever since. It was used by Wm. Larsen Sr. in a trick called “Finger Prints” from The Sphinx, Vol. 22 No. 5, July 1923, p. 149. While Edward Bagshawe is often credited with the principle, he didn't publish his application until Twenty Magical Novelties, 1930, p. 57.
The presentational format of “Out to Lunch” was invented by Clare Cummings and Bob Ellis, used in their appropriately titled marketed trick, “Out to Lunch,” 1946.