No problem
Yep, that's the stuff. I never detailed any method, but I've used it on headlights and my rear bumper after a small paint repair.
I start with either 200 or 400 grit, depending on the condition. If there are actual divots in the plastic from rock strikes, I'll use the 200 as it is very aggressive. Otherwise, a moderate sanding with 400 to remove all of the old clear, then 800. I don't recommend going much higher than that, but maybe my experience is different from others. All wet sanding, BTW.
The 800 leaves something for the clear to bite.
I've also never had any luck with multiple coats. I usually just lay on one thick coat, which is tricky to do without runs, but once you get a feel for it, it gets easier.
The bottom line? If I had to do it again, I'd probably just ask a paint shop. It's a pain and so many things can go wrong.