Before coming to New Spain, Elizondo fought in the battlefields of Italy during the War of the Austrian Succession (1740–1748) and Seven Years' War (1756-1763). His main field of action was New Spain, where he served between 1767 and 1771.[3]
In 1767, Elizondo was sent with 500 soldiers to Sonora.[4] Between 1767 and 1771, he served throughout New Spain, fighting against the Seris and the Pimas in Mexico and Southern Arizona. He published a book about his experiences in the region.[3]