I've checked several online dictionaries, but can't find one that makes the specific distinction shown here using two screenshots of the (source unattributed) initial summary returned by googling...
define "have a thing for"
define "have a thing about"
I'm sure there will be some native speakers who don't recognise this distinction, but it's one I've always made. And I'd say the fact that Google gives it top billing supports my position.
And this may be purely my own opinion, but I think that we're far more likely to say someone has a thing about something (rather than for) when the intended sense is that they derive some kind of deviant sexual pleasure from it. That sense is partly positive, partly negative (cf: "forbidden pleasures"; nice to experience, nasty to talk about), which may go some way to explaining why there's not a straightforward split between the two prepositions as regards good / bad connotations.