I'm looking for the same things (and according to my little experience, INFJs are a perfect match, perhaps for an INFP it would be ENFJs, but definitely a 4 idealist would be really at ease with another idealist).
I had this conversation with a friend of mine who didn't understand where comes from this need to be deeply understood by a significant other(and also the need of putting oneself in the other shoes to understand him/her totally). He told me I was telling myself a whole story, I was "outside", putting labels and words, instead of being "inside" and actually live it.
So the trick is I think the 5 wing causes to withdraw in the story we built on the relationship, despite the fact we need to connect on an emotionnal level first.
IMO, when we're not mature enough, we tend to gravitate towards cold intellectual mates (like 5s, quite comforting at first but in the long term it was frustrating) or on the contrary some sort of "shallow feelers" (and it'll be frustrating in the short term because of the "you think too much" who will pop up very soon). It's all about balance, your mind needs an interesting and stimulating partner of course but the real connection comes from the heart...
[So, I'd say - ironically - "don't think too much" about MBTI types and trust your guts. ]