I have a notion that my Great Great Grandfather (an Irish Catholic) was a patricio but am still trying to find the real reason he never came home in 1847 after voluntering to serve in the US Artillery out of Tennessee ...
The sea chantey, General Taylor, was likely sung by Liverpool and New York Irish with little love for the established order -- whatever side of the Atlantic. So Santianna won the day their songs ...
According to Hugill (genuflection optional), he categorizes the chantey as the unhistorical story of Santiana:
"Quite a few British seamen [Irish?] deserted their ships to join Santa Ana's wild and ragged army ..."

Hugill records an old west version as follows:
"Ol' Santiana, ol' Santiana! Ol' Santian, ol'Santiana! Ol' Santiana . . . Santiana gained the day, Hooray, Santiana! Santiana gained the day, Upon the plains of Mexico, Mexico, Mexico."

Titles include "Santiana," "The Plains of Mexico," and "Old Santy Ana."
Huzzah!
Brian