House is a fictional character, his personality in the show does only work, because it plays well together within the environment its put in and the other characters it reacts too. Most of the time fictional characters aint good to compare for type, although they can set nice ideals

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If you want to find out about p or J, you really should look into function analysis. The 4-letter type code is only a description for function distribution, many people confuse that.
If you are for example ENTP, you would have:
Extraverted Intuition
Introverted Thinking
---
Extraverted Feeling
Introverted Sensing
The first 2 indicate your primary functions, while the last 2 indicate auxiliary functions. How you use them in life, should become from secure on the top, so the first function, to insecure on the bottom, the forth function.
N and S, so Intuition and Sensing are perceiving functions, while T and F are rational functions. So while T and F are the CPU of your computer that processes the information, N and S are different mechanisms to gather information, through concious or unconcious means.
So, if your 1st function is a perceiving functions, your are in terms of MBTI a p and if it is a rational function you are a J.
To associate that J's are more to be the leader type or whatever associations there are, is not good. But to have a rational function as your primary one brings certain advantages with it when it comes to being sure about a decision. While a perceiving function for example, can't stop taking in new information or looking for new, before it makes a decision. - (on the other hand it can mean that J's are to quickly or strictly to make a decision)
And from that point on, you can draw all kinds of new connections
