Simple answer, Jane is INFJ because he's always in his head and he's always listening, and not thinking his thoughts out loud. ENTP's come to their conclusions by saying them, not internalizing them, the whole Ni versus Ne differentiation. He's DOMINANT Ni and that's it, it's simple really. Patrick Jane has to tell someone what he's already come up with and share what he already knows (his step ahead), whereas an ENTP will discover the answer by talking it through. INFJ is subtle, and ENTP is overt, and Jane is the former.
ENTP's pick the brains of their peers for everything and make their next move by asking everyone for advice in a group, wheras Jane is off on his own all the time, doing his own thing always a step ahead with his intuitive leap (like Columbo playing dumb), always wanting to isolate the group from what he's doing and manipulate situations away from the group, without their consent, all by himself, like the loner INFJ. "With" the group, but not "of" the group. He's a very typical INFJ in already coming to a conclusion and then manipulating circumstances to prove the intuitive leap, while being very covert, subtle and unsuspecting, which is NOT a trait of ENTP's at all. ENTP's are too OVERT in their approach (not that INFJ's can't be), from what I've read and from experience. Notice how he lets people talk and will only interupt when a point is needed to be made? ENTP's are dismissive to everyone they think are dumb and not with the program and will go on and on and on, and Jane is not like that, he hears everyone out, as that's the whole way of uncovering the truth, by listening. ENTP's like the concrete, and don't deal well in the grey areas of life, and often get hung up on minutia which is manifest in a lack of follow through, ie, time to start a new project. Also, ENTP's are much more capable of letting go of the past than INFJ's who can't let go of the past for the life of them like Jane when it comes to Red John. Notice how he won all that money when he went gambling, and then thoughtfully bought everyone something they wanted, and then anonymously donated the rest to charity? Super INFJ loner mentality where money isn't as important as the greater good, a means to an end, not an end in itself. Patrick Jane also avoids argumentation and debate and attempts to replace it with dialogue and discussion when talking to his peers, but allows chaos and debate when talking to suspects. The strong differentiation between those who are with me and how I treat them and those that are suspect. It may be confusing because INFJ's and ENTP's are both very dismissive to people, with statements like, "No, it's this, nothing more." Finally, back to my main point towards INFJ is the dominant Ni and secondary Fe and prophetic characteristic that goes in hand (probably what you were first thinking IDK) with all INFJ's!
So Jane can be summed up in Ni, loner, can't let go of the past, listener, idealist, giving, simplistic, quiet, in headspace, empathetic, relational system analyzer, can't be fooled, humanitarian. Like what it says here:
INFJ Profile
Anyone have anything to say about Cal from Lie To Me being an ISTJ with the hard sciences? Is he more of an INTJ than ISTJ? More of a science builder than a science analyzer? Cal sniffs out the truth like a detective with cold hard science, as in the ISTJ, so that's why I staked my claim on ISTJ. Your point TReflection, about the science becoming repetitive is exactly what I meant by having an expiration date. Unless Lie To Me comes up with a more genuine macroplot, the show will get stale and dry because we've all seen Sherlock Holmes and CSI.