Those interested in the St Patrick's Battalion (Los Patricios) should read "Shamrock and Sword," by Robert Ryan Miller, Prof. History, California State Univ. at Hayward.
The Battalion was never entirely Irish (est. between 40-60 %). One of the posts seems to suggest that (Sgt.- U. S. rank) Capt. John Riley was just a name in a song. He was real. After the failure of the Mexican War effort, he was court-marshalled, but was not hanged, like a number of the Battalion members were, because he had deserted prior to the official declaration of war. He received 50 lashes and was branded "D" on his cheek. He did not remain in Mexico as many did, but returned to Ireland.
After the War, a battalion of Los Patricios continued in service for a short while, patrolling to prevent attacks by bandits and Indians. Mexico lost half of its territory in the war, a point which still rankles.
A good, very brief history is given on this Univ. Texas website: