In my last relationship the opposite was true. I don't know about how it's felt on the other end, but I like the feeling of being close to and open with someone.
I think though that I had a family that was very close emotionally and that helped. I also had an ENFJ mother, which probably made it easier to share my thoughts and feelings and to feel understood. It's true though that it takes awhile for people to get to know the more vulnerable parts of me, but it's not a conscious thing really at all. Sometimes I don't even know what all's in there until it comes out. It's just that the more comfortable I feel around someone and the more interested they are in knowing, the more of me they'll see. Similarly, the more miscommunication there is, lack of interest or devaluing of what matters to me, the less I show. Again, that is not so much conscious as unconsciously done.
I feel much better when people know me well, but I don't want to impose myself, and especially the more difficult parts of myself on them until I am pretty sure that both they and I can deal with it alright. That's one of the reasons why you won't hear an INFJ telling you their most candid thoughts until there is a lot of trust built up, especially if those thoughts or feelings are negative and could impact the relationship. With my ENTJ friend, around the end of the second year of us spending all of our time together, I finally told him that some things he was doing seemed really inconsistent to me (other friends had been frustrated about the same and told him, which opened up the discussion after another incident) and also told him that I was frustrated that there wasn't a lot of give and take in the friendship. Everything was on his terms.
The matter of fact way he handled it, and the openness and interest he expressed in knowing actually made me feel the closest to him that I ever had. 15 years later, we are still in touch. He is married, with a baby, and so I on purpose have not regularly skyped or called because I don't think I'd like that if I were his wife, even though I have no interest in him (but he did in me at one time).
With my ESTJ, his ability to get me to try new things and his skill as a teacher made willing to take risks doing things that I normally wouldn't in front of someone until I had known them for many years. He had a great way of explaining things without making me feel foolish and he loved sharing new skills or getting me to try food that I normally wouldn't enjoy. He also made me venture into social settings that I normally would avoid and made them an enjoyable experience.
That made me feel an instant kind of attraction for him from the very start. On the other hand, the way he handled conflict and his need to not hear anything that could upset him emotionally, as well as his need to appear emotionally invulnerable (to the point of actually retelling events to myself and others in such a way that I began to question my own sanity until finding objective evidence that my initial impressions and memories had indeed been correct) threw up more and more barriers between us until there was very little left to talk about. There was too much unresolved conflict and I did feel like I even knew what he valued about me. In fact, the very thing that had attracted me became a sore point, as there was no skill that I had (even ones that he was trying to learn), where he was willing to put himself in a vulnerable position to learn from me, yet expected me to put myself in that position all of the time.
Most people that I've liked (and therefore wanted to open up to) are people that are extroverted (are very comfortable socially and are good at making me feel comfortable in their social world too), people that are clear in their interest (rather than leaving me wondering and unsure and therefore tentative about opening up), and people who verbalize what it is about me that they like (I can see a role for myself in the relationship and know how to make them happy). Something that I more seldom experience, but which does make me open up is someone asking me questions about myself and also about how I think without debating, but just to gather information and understand me. The process of answering those questions also helps me understand myself and the world around me better, and anyone who can make that happen is someone that I'm going to value and want to be open with. One of the reasons that I enjoy this forum is that it is a catalyst for me to answer questions or state opinions - something which I do less openly and comfortably in the real world and something that many people aren't that interested in there. (I'm not implying I'm unhappy with them, but just that it is rare to have someone really want to know what makes you tick).