There are big secrets and little secrets.
Little secrets I do keep back a bit on purpose. In relationships its easy to feel a bit trapped, and keeping things back is a way to feel more independant. But little secrets aren't much, they just keep a bit of mystery (and excitement I guess) and often when I feel more invested I do let the other person know more about me, my hobbies, friends etc.
Big secrets like past traumatic experiences, medical issues and the like I didn't consider anybody's business except my own. I didn't even consider sharing. Seemed like a huge risk with no reward. But recently I did share with someone special and it felt really good. Like a load off my back. Sharing isn't really a goal or something I usually consider, but if the other person is trustworthy and persuasive then I can open up on the bigger stuff as well.
I think its probably described okay with hidden agenda Fi. SLI's won't feel its their job to get closer through sharing, and are a bit hit or miss with feeling that closeness (sometimes they are aloof and distant, other times much too forward and over the top). But they can feel lonely without somebody to entrust their sensitive soul with, a treasured bond with someone else. Its not so much a life goal, but they definitely care about it. That being said I read somewhere SLI's usually just get a pet and thats enough of a trustworthy bond for them. So I guess how much they feel the need to open up is dependent on them and the other person/cat involved.