Green’s Dictionary of Slang

(US) the vagina.

1925		E. Field ‘A French Crisis’ in Facetiae Americana 19: What shall I term that slimy pit-like orifice of sin, / [...] / A- tuppence, twitchet, coney, commodity or nock.
1950		in V. Randolph Pissing in the Snow (1988) 97: I seen his hand reach over and touch your twitchet. [Ibid.] 138: He began to tickle her twitchet.