GIG,
a Nose; also a Woman's Privities. Snichel the Gig, fillip the Fellow on the Nose. A young Gig, a wanton Lass.
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Entry taken from 1736 Canting Dictionary, by Nathan Bailey.
The Vulgar Tongue originally collected by Grose, 1811.
Also see examples in Canting Songs and Slang Rhymes collected by John S. Farmer (1896).