Are you kidding? a quiet activity that keeps him entertained for long periods of time? I would ENCOURAGE closet time!!!
I had to laugh at this because that is exactly how I feel! he wants to play in the closet and I'm like WHOOOOO HOOOOO, off to BW for twenty minutes!!

I personally have no problem with it - as all of you have said, he's having fun, doing something interesting to him (who knows
why it is interesting but hey if he likes it why care?) He likes opening and closing the door (it slides) and sitting in his little "fort" -- yes DH makes lots of forts with him, most every night really, using a variety of things (quite often the clothes maiden with bedsheets hung on it in the living room and he will just sit in there doing NOTHING for ages. If DH does not mind this why does the closet bother him so much?

Kids like small spaces - Nicole I love that Ava likes going into the kitchen cupboard, soooo cute! No idea why it bothers DH though? I think he just thinks it is strange and anti social?
But then it sounds from other posts that Mini-mashi finds something he wants to do and then becomes fixated/determined about it, and that is just part of his character.
Um, do you know my child or what?! Yes yes yes, everything with intensity - exactly like his father, so again I ask, what's the problem!
I suspect that one of the reasons he likes it is because the first time he went in I probably said something like "Oy, you little stinker what are you doing in mommy's closet!?" and laughed and went and tickled him in there which to him meant "hey this is something funny" and now can't drop it. He's like that...do something once and have fun with it and you are FOREVER having to do it again. And again. And again.....
Little stinker!