had a similar issue but it was on my 86 IROC-Z. My 3rd brake light is outside and high up on the rear glass. My cousin who was a Black Hawk mechanic for the US Army checked it out. He ran a battery of tests on the strip of metal that housed the 4 light bulbs. Results were that the metal was structuraly non conductive. Even though the metal seemed to look flawless, it was no good. so I went to the junkyard and took off one from a Trans Am. Sure enough the Trans Am one worked.

The same issue might be occuring with yours.