This principle was used at least as far back as the 17th century. It is explained briefly and incompletely under the heading “Pour faire qu’en tirant une carte hors du jeu, il s’en trouve une autre sans que l’on l’aperçoive” in Trésor des secrets inestimables, pour la conservation du corps humain by Seigneur Rondin, 1630, p. 10. Other descriptions of the trick appeared in two anonymous, unpublished manuscripts of the period: Sloane 424, c. 1600s, p. 160 of the Pieper translation; and the Asti Manuscript, c. 1700, p. 58. These manuscripts were published in Gibecière, Vol. 5 No. 2, Summer 2010, p. 141-172, and Gibecière, Vol. 8 No. 1, Winter 2013, p. 29-234, respectively. The methods didn't use a rubber band, of course; instead, they used a card folded in half, and a finger or thumb across the pack to conceal the seam.
The trick surfaced again in the mid-nineteenth century, described with a half-card rather than a folded one in the trick “Hold it Fast” in the 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 marketed trick, appropriately titled “Out to Lunch,” 1946.