Green’s Dictionary of Slang

John Willie n.

[var. on John Thomas n. (1); note willie n.5 ]

the penis.

[US]Maledicta IV:2 (Winter) 189: The reverse process of this [...] depersonification of the penis is its personification [...] as Dick, John Thomas, J.T., John Willie, man Thomas, etc.
[UK]Partridge DSUE (8th edn) 625: since ca. 1930.