24 year old headlights. FWIW I got pretty good results by wet sanding with 1500 then 2000. I sanded with the 2000 a good long while, back and forth. Then used polishing compound on a foam pad. Topped with a coat of Mother's Back to Black. Edit: They actually look almost new.
I used to use Novus plastic polish - the same stuff you use on an NA Miata vinyl rear window - to refresh the lights on my 2000 Tundra. Took just a few minutes with a microfiber cloth and nothing else. Probably had to do it every two years, I suspect a UV protectant finish had failed. Boy, did it make a difference.
The WJ Jeep, though, fogged on the inside. Nothing you could do.
In reply to Keith Tanner :
Just Googled "Novus plastic polish" and saved the link
It's good stuff to keep around and lasts forever. My bottles are from the 90s :)