As I said it is my suposition that General Taylor was sung by the deserters, the San Patricios.

I base this on a few things.
In the liner notes for Great Big Sea's "Play" it is stated that the song was about a deserter, but if you look at the Storm Along family of shanties (Of which GT is a member)it seems more likely that the deserter connection is that it was a version sung by them not about them, and over time the story became confused. The only reference to deserters in the Mex/Am war I can find is The San Patricios.

You can not deny the connection of the shanty General Taylor to one titled Santa Anna, where Zachary Taylor is mentioned by name, it is the same tune. (Santa Anna he gained the day, Zachary Taylor he ran away... historicaly inaccurate but hey, it's folk music!)This connection between the songs is illuminated in Stan Hugil's Book - Shanties From The Seven Seas

As to why they would desert, references site the mistreatment of the Irish Catholic Soldiers by the mostly non-catholic officers of the US military. Mexico being a very Catholic nation would be a likley haven for such men, and they might be more sympathetic to the cause of such a nation.

So there :P

Nick