Never heard it sung that way, but Scouts sing some odd songs and versions.

Note- The version printed in Fife & Fife from Woody Guthrie MSS is in thread 61371: Early in the spring
The song appeared in print in Lomax, without notes; the version with chorus posted above by Jim Dixon.

In the revised edition of 1928, Lomax and Lomax published a different version, one of thirteen, from J. E. McCauley of Texas (no date), with music from the Cowboy Band, San Angelo, Texas. I will post it later today.
It has a refrain:
I'm going back to Mexico
Where the longhorn steers and cactus grow,
Where the girls are good day after day
And do not live just for your pay.

There seem to be many versions.