It is indeed a Nuttall's - also identifiable by the red crown ending well before the forehead. Ladder-backed is also found further east on the desert side of the coastal mountains, Nuttall's is common locally in the area around the Safari Park.
@LaughingDove Yep! I feel like a lot of California birders probably take them for granted due to how prevalent they are in most places, after just walking around my school for a few minutes I sometimes hear 3 individuals.