I really want to improve the looks of my taillight lenses. They are not offered reproduction that I can find and mine are dull compared to cars at shows that can get repros. Is there any method to revitalize them?

 

Clean them very well with dish soap and a toothbrush, then have them clearcoated. Use real paint, not a parts store spray bomb.

 

I'd use one of those kits designed to restore headlights.

https://www.summitracing.com/parts/tes-7000045522

 

For oxidized plastic lenses, you can follow a fairly simple process. Get yourself some 1000 and 2000 grit sandpaper and a bottle of plastic lens polish (auto parts store). Start with the more aggressive of the two and WET sand (NOT dry) the lens. Follow that up by WET sanding with the less aggressive. Finally, use the lens polish to clean them.
This process works well and is pretty inexpensive. Keep in mind they can/will oxidize again depending on how much exposure they have to sunlight. You shouldn't have to go the sanding route again for several years of normal exposure. An alternative is to coat them with a quality clear as mentioned above once you get them polished. That should block the UV and keep them looking good for years.

 

When I did the marker lamps on the Hurst/Olds, I used 2 or 3 different cutting grades of Meguiar's liquid polish. They gleamed like new. They were, of course, nice flat pieces that didn't have the recessed areas the 1967 taillight lenses have.

A variable speed dremel tool with a medium cut buff might make the job easier.

 

Eastwood should have the polish and the polishing tools.

 

Best way is the method explained by Acavagnaro. But sometimes the lense is too detailed then I would use the method explained by Rocketraider.
I have used both with very good results.
But in the end a good cleaning with a mixture of Alcohol/water to remove any residue before final top coat.
If you don't have access to a good Automotive clear, the next best thing is to apply a good paint Ceramic Coating. I'm talking about the stuff detailers use as automotive paint protection. You can get it at any good detailing supply store (Autogeek). This stuff lasts for years and easy to apply and reapply.
Directions for use is wipe on buff off. But that's for flat paint surfaces. If you have a detailed piece I apply using a cheap airbrush from HF or cut a piece of a sponge buffing pad.
You would be amazed at the protection it gives and ease of use. It's the only thing that keeps my old plastic headlights from fading in the Florida sun.