Green’s Dictionary of Slang

evesdropper n.

[pun on SE eaves + eavesdropper]

1. the penis.

[UK]Urquhart (trans.) Gargantua and Pantagruel (1927) I Bk I 44: And some of the other women would give these names, my Roger, my cockatoo, my nimble-wimble, bush-beater, claw-buttock, evesdropper, pick-lock, pioneer, bully-ruffin, smell-smock, trouble-gusset, my lusty live sausage.

2. (also eavesdropper) a robber of hen-houses.

[UK]Grose Classical Dict. of the Vulgar Tongue.
[UK]Lex. Balatronicum.
[UK]Egan Grose’s Classical Dict. of the Vulgar Tongue.
[UK]G. Kent Modern Flash Dict. n.p.: Eve droppers, vagabonds who rob hen roosts.
[UK]Flash Dict. in Sinks of London Laid Open.
[UK]Duncombe New and Improved Flash Dict.
[UK]Barrère & Leland Dict. of Sl., Jargon and Cant I 343/1: Eavesdropper (American thieves), a chicken thief, or low sneak or thief generally.
[Aus]Crowe Aus. Sl. Dict. 227: Evesdropper, a mean thief; a chicken-stealer.

3. a burglar who lurks outside a house waiting for the chance to break in while the owners are absent; thus a petty thief.

[UK]New Canting Dict. n.p.: eves Dropper a Villain that lurks about the Doors of Houses, to watch his Opportunity to rob or steal.
[UK]H.T. Potter New Dict. Cant (1795).
[UK]G. Andrewes Dict. Sl. and Cant.
[US]Matsell Vocabulum.
see sense 2.