Songs with the chorus "Jenny gone away" are documented 1830s-40s for river boat rowing and corn-shuckings by Black Americans in Georgia, Virginia, and South Carolina. Later, a halyard chanty form turns up as "Johnny's Gone Away." It was a widespread trope. Let's not let Sharp and Terry (who collected similar stuff) and Hugill (who pretty indiscriminately incorporated prior printed material) give an illusion that this was a static piece of work.
To an extent, the idea of "Tommy's Gone Away" as a discreet item, seen as a variation of another discreet item, "Tommy's Gone to Hilo," is a construct of the collectors, created from a very small sample.