This was probably referring to John Mulligan, who is referred to in this discussion of the population at Branciforte, adjacent to the mission of Santa Cruz:
The total population of Spanish or mixed blood, known as gente de
razon in 1820, was estimated at something over 3,000 souls; and of
foreigners not of Spanish or Indian parentage, twelve; of these Thomas
Doak and Daniel Call, who came in 1816, and Joseph Chapman in 1818,
were Americans; John Gilroy in 1814, and John Rose in 1818, were
Scotchmen; Thomas Lester in 1817, and I. Thomas in 1818, were
Englishmen; John Mulligan in 1814 or 1815, was an Irishman; Jose
Bolcof in 1815, was a Russian; Juan Cristobal in 1816, M. J. Pascual
and Fisher or Norris in 1818, were negroes.
The above quote appears to be an excerpt from Memorial and Biographical History of the Coast Counties of Central California.
Mulligan is also discussed in more length in The California Padres and Their Missions
...along came Irishman named John Milligan or Mulligan who had
stranded in California from some ship and couldn't get away.... he and
Padre Luis struck up a friendship the Padre to drive away his ennui I
suppose and also because he had a philological turn and had already
picked up a couple of Indian languages conceived the notion of
Mulligan to teach him English...