Green’s Dictionary of Slang

twitcher n.1

[? play on ety at twitch n.2 (1), i.e. a noose or loop]

the vagina.

[UK]‘The Girl & Her Twitcher’ in Facetious Songster in Spedding & Watt (eds) Bawdy Songbooks (2011) III 260: He prattled and toy’d, / But still she replied, / ‘Pish! lewt go the hold of my twitcher’, poor girl.