Is Tuesday named for a one-handed god?
"penis," 1933, slang, probably from whangdoodle, an earlier term for "gadget, thing for which the correct name is not known." Many such words (thingy, dingus, etc.) have been used in slang for "penis," not because the actual name was unknown, but because it was unmentionable. Another possibility is that the slang word is a variant of whang "large, thick slice" (1630s), which earlier was used in the sense of "thong" (1530s) and is itself a variant of thwang, an alternat form of thong (see thong).
[1935+; probably fr whangdoodle, ''something of uncertain name, gadget''; many such terms, like diddlywhacker, dingus, doodle, and thingy, are euphemisms for the penis]