Green’s Dictionary of Slang

ballcock n.

the penis .

1834		‘The Ball Cock’ in Randy Songster in Spedding & Watt (eds) I 204: She tried it and her sorrow was soon on the wing, / She found Mr Doall’s ball-cock just the thing / [...] / Says she, since your ball-ock you’ve given so free, / No other cock shall ever serve me.
c.1850		Peeping Tom (London) 12 48/3: [advert] merry chaunter — The Plumber’s Ball Cock.