The dedicated kits from 3M, Meguiar's, etc, is much better, but a nail file from the supermercado will get you a long way if the lamps are really bad. But the coarsest side is too coarse and the step from the second coarsest side to the polishing side is too big to remove the scratches. And toothpaste makes it worse again. Vinegar and baking soda applied by hand may help, but I couldn't see any big difference.

 

When I bought Black Bess the off-side headlight was noticeably more tarnished than the near side but before trying one of the kits I decided to have a go with whatever came to hand first. So, TCut was the first choice which did quite well but nevertheless was not good enough, next came Solvol Autosol which worked very well in my opinion. The downside however is that both needed to be blended with considerable amounts of EG.

The good thing about elbow grease it that it's always on hand.