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I have found the best way is to remove the license plate, then the backup lamp assembly. Remove the inner tail lamp housing and then reach thru that hole to get to the lamp socket. All of these housing use a 10mm nut. It helps if you have small hands as it's not real easy to get behind there. You may want to wear some gloves as there are some sharp edges. Be prepared to chase tools that get tossed across the garage from frustration. Beer helps here...
A good project is to remove all of the tail lamp housings and replace all of the bulbs. Why?? It will just be a matter of time before other bulbs can fail. When the original bulbs were installed, GM used a grease to help prevent water getting into the sockets and cause corrosion. By now this grease will be very hard and pretty much useless.
YOu can clean the inside of the housings by squirting a small amount of liquid soap and hot water in the housing. Let it sit for a few minutes, shake very well then drain and rinse. Let them dry with the opening face down. You can also clean the opening in the facia while you wait.
Remove the old bulbs and clean both of the socket contacts and the walls of the socket. Get some dielectric grease and coat the contacts and the bulb socket and reinstall. I use Sylvania 1157LL (long life) bulbs for replacements.
I reached up from underneath, arm between muffler and plastic fender. Use a palm ratchet with a 10 mm socket .The fender is somewhat flexible. It is all by feel and your arm will be bruised and sore for a couple of days. I wonder if the stiff ride of the Corvette leads to short bulb life.