The third brake light on the '86 to '96 Corvettes runs off of a separate switch from the other brake lights. Check this thread at the Corvette Action Center: http://www.corvetteactioncenter.com/forums/c4-technical-performance/126533-new-brake-light-issue.html
Make sure you have power to the lights when applying the brakes. If you do, check the ground and the connections. Spray the sockets with WD-40 and use something to scuff the connections. You may have power at the fuse junction, but at the end of the long wire run, do you have it there. Make sure you have a good ground when you test for power. I'd spend the extra $5.00 and get new bulbs. If the old ones are good, they you have spares.
Search Chevrolet Corvette Questions
Chevrolet Corvette Experts
Related Models For Sale
Used Cars For Sale