I don't know about Simon Baker, the actor, but his character, Patrick Jane, is definitely not an INFJ. Or at least in my opinion. He's too motivated and willful and his pace is too quick. He is also an extrovert besides. He hates spending time alone. That's the whole point of him camping out in C.B.I headquarters. Being left alone with his thoughts terrifies him.
I've always classed him in the EXTP category and he kind of reminds me of Bugs Bunny in a way. He makes things up as he goes along, doesn't commit to one theory or another, and my God, is that man ever fond of show-boating. He takes immense pride in his mental acuity and takes every opportunity to indulge in his curiosity and exercise his brain. Yes, his subject of interests are people and their relationships, but his methods and intentions are not to get close to them, but to extract information to benefit him. I should say the fact that he's a 'Mentalist' to really tip this off. His approach is entirely method-based rather than holistic. He's trained himself to interact with people a certain way.
Despite the tragedy of his wife and daughter's murder, he's still a con-man at heart and his focus is revenge. He sees the CBI as a means to an end and has even told Teresa that if she stands in his way, she will regret it. He also has no qualms about ruining people's lives for a cursory piece of information and he dismisses it as them deserving it. He also has no issue with giving the C.B.I a hard time, or even giving Teresa trouble despite all the help she's extended to him over the years. He doesn't really stop to consider the emotional impact that his schemes might have on other people unless it suits him.
As for dominant functions, I would probably lean more toward Ne over Se given how his emphasis is more on the subject's significance, past and meaning rather than just its basic fact. He's also not really one for action or getting his hands dirty. He prefers seeing everyone else running around and falling into his trap than to get directly involved.