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]