There are loads of ways to cure the miserable yellowing of our ageing headlights and even more threads describing them. Toothpaste is popular, sanding down sounds scary and I've always buffed mine with a pad on a drill and polish...
Today whilst attending to some other detailing. I had a can t.cut in my hands and thought I wonder...
Two mins later the lights looked (almost) brand new. So results might vary, but this is definitely worth trying! I think you might be surprised & pleased.
Any of those polishing compounds will work - basically very very fine liquid sandpaper, takes the top UV yellowed layer off, key thing is to then coat it before the next layer yellows.
Yup, I've used T-Cut for this purpose for years. It works very nicely. I currently have a kit that I got from my local car parts place a little while back. It has a different bottle of stuff in it. It doesn't look much like T-Cut but it will just be the same principle of a suspension of abrasive particles to take the top layer off. The kit came with a sealing spray to delay re-yellowing.
Incidentally, toothpaste works for the same reason as T-Cut does. It is also a suspension of fine abrasive particles.
Headlamp de-yellowing is easy enough (in my opinion). I find the crazing/cracking of our older headlamp plastics more annoying (mine are not too bad, but there is a little bit going on and I have seen some really bad ones) and, unfortunately, with them there isn't really a fix (that I am aware of) other than replacement.