Depends on the flow of the conversation whether I would index first or after, "He doesn't/don't care." or "Doesn't/don't-care he" . For myself, "I don't care", I tend to sign, "Don't-care I".
I remember my first ASL class, the teacher was teasing me and at one point he used an open curved 5-hand near his behind and moved it outward. I had no idea what he was expressing so asked, "Are you saying I have a big butt?". He laughed hard and explained that he meant I was rich (ie: a wallet in my pocket was very fat/stuck out far). I learned three things that night ... my teacher had a great sense of humour, ASL is indeed very conceptual, and always ask when you don't understand - never just pretend you do (if I had just smiled and nodded and never asked, I would have gone home and complained to my husband that the teacher called me out on being a fat a** LOL ).