A few years ago...02-ish,I stumbled upon a way that works incredibly well in just a few seconds.
I've been detailing cars/trucks on the side since I was a teenager.One day,I was detailing a friends Lexus ES300 that had 220k miles on it.He had complained in the past that he always needed to use his "high beams" cause his headlights were so yellow and you could'nt even see into the housing.
While I was in the process of buffing the car...I got a little over-spray of compound on one of the headlights.So,instead of taking a rag and wiping it off...I just ran the buffer right over it...and in that 4-5 seconds,it made a huge difference in how it looked.So I put a little more compound on and ran the buffer over it for a few more seconds...even better!.In less than 5 minutes of buffing it quickly...it looked nearly brand new...all the yellow was completely gone,but there was just a hint of etching that I probably could've gotten out if I kept going,but the cover was getting quite warm at that point,so I called it "good enough".
This pic shows a foam pad...I've found for doing headlight covers,a wool pad at 1000rpm works the best....and keep the buffer moving at all times!!!...or you will melt the plastic in a blink of an eye.

I've used a couple of the headlight restore kits...and they're not bad,but the buffer method is just sooooo much faster,and alot less work