I found sheet music for this song at University of California, Berkeley, described thus:

HE GETS THERE JUST THE SAME
Words by Will. M. Peters; music by O. Langey.
San Francisco: I. L. A. Brodersen & Co.,/Windsor Music Co., 1886.
'As sung by "Canby the Plumber," in the "Tin Soldier" '

Lyrics are almost identical to those posted by Bob Coltman above.