Sounds like a corroded ground to me. Typically these lights ground directly to the frame. But over the years, corrosion will get under the bracket and increase the electrical resistance to ground, causing the lights to get dimmer.
I've had the same problem with snowmobile trailers. Ultimately, I ended up running a separate ground wire to each tail-light and running light and ran it all the way up to the ground wire at hitch connector.
In your case, you'll probably just need to clean the rust under the light's bracket and probably solve the problem. Also check out the engine-to-body ground. Those also need attention periodically, especially in 'salt country'.