1856, from phrase to speak with one's tongue in one's cheek "to speak insincerely" (1748), suggestive of sly irony or humorous insincerity, perhaps a stage trick to convey irony to the audience.
Hem! Pray, Sir, said he to the Bard, after thrusting his Tongue into a Corner of his Cheek, and rolling his Eyes at Miss Willis, (Tricks which he had caught by endeavouring to take off a celebrated Comedian) were these fine Tragedies of yours ever acted? [anonymous, "Emily, or the History of a Natural Daughter," 1761]
This arietta, however, she no sooner began to perform, than he and the justice fell asleep ; but the moment she ceased playing, the knight waked snorting, and exclaimed,—'O cara! what d'ye think, gentlemen? Will you talk any more of your Pargolesi and your Corelli ?'—At the same time, he thrust his tongue in one cheek, and leered with one eye at the doctor and me, who sat on his left hand—He concluded the pantomime with a loud laugh, which he could command at all times extempore. [Smollett, "The Expedition of Humphrey Clinker," 1771]