Nick there simply were not enough deserters from the US army of the day to account for anything vaguely related to folklore as here discussed.

Re desertion to Mexican forces from the US calvalry, your evidence?

I find none and am not surprised, why would they?

Desterters did have an impact in the south elsewhere. During and the battle of New Orleans thousands of the British rank and file simply ran away into the bush. Most of these ended up in the hill country, and most of them were English ... so much for politicking... but I must say I can harldy blame them for running away, what with being shot to hell by an army of the native population of Mestizo, Black slaves and the few whites that lived in the south at the time.

Song The Battle of New Orleans writ by a descendent of one of the run aways Mr Jimmy Morris ....