The tune has been used for a number of bawdy parodies, some of which are given in Ed Cray, "The Erotic Muse."

Cray, citing Fuld p. 516, comments that the tune (Gambolier) appeared in "Carmina Yalensis" in 1873, and "three years later was borrowed by vaudevillian Ed Harrigan for a textually unrelated comic stage song, "Dunderbeck.""

This would place the origin of the song in 1876.
Harrigan (died 1911)was part of the famous team, Harrigan and Hart. They joined forces in 1870 and in 1873, with David Braham, produced the first of the very popular "Mulligan Guard" series, a one-act vaudeville burlesque presenting a caricature of New York life with such racial groups as Irish, Germans and Negroes, playing on their speech patterns, behavior and mannerisms. David Braham contributed songs, Harrigan the lyricist. The Mulligan shows were prominent in New York, especially from 1879-1885, ending when the team broke up.
www.theatrehistory.com: Musical Theatre
The article extracted above was published in "The Complete Book of Light Opera," Mark Lubbock, New York, Appleton Century Crofts 1962, pp. 753-756.
Also see: Braham

(Now will someone go to the NY public library and check specifically for the song "Dunderbeck" in the Mulligan plays)

"The Pioneers," in Cray p. 228-230, and also in Randolph-Legman, sung to the tune "Son of a Gambolier," is in the DT. It has the memorable first verse:

The pioneers have hairy ears,
They piss through leather britches.
They wipe their ass on broken glass,
Those hardy sons-of-bitches.