By accident I ran across a documnent in pars website where in 1798 the governor or Yucatan was "Arturo O'Niel."
http://pares.mcu.es/ParesBusquedas20/catalogo/description/64238?fbclid=…
I looked him up in yahoo and find out that quiet a few Irish were serving for the spanish crown:
https://en.wikipedia.org/wiki/Arturo_O%27Neill?fbclid=IwAR3-RraF7lS1s5r…
St. Patrick's Batallion
While not quite as old as 1798, I think people in Mexico who find they have Irish ancestry would be interested in researching "Los Patricios" or St. Patrick's Battalion. During the Mexican-American war, the Patricios were an artillery division which proved very effective.
As fellow Catholics, the Patricios fought on the Mexican side. With the eventual defeat of Mexico, many of the Patricios remained in Mexico and most were granted land.