My third brake light dosen't work on my chevy s10 94'

I had a similar problem with my 1994 S-10 LS extended cab. Both tail brake lights worked fine. I removed the 3rd brake light cover and tested for voltage at the steel center of the two rivets and found the positive (driver side) negative (passenger side) were good. I checked the two metal strips that send power to bulbs and found the positive side was open. Seems the flared side of the rivet was not making contact with the metal strip. I bucked the rivet with a punch and hammer and it took care of the problem.

Try seeing if you are getting power to the scoket. then try the wires going to the scoket