97 Saturn SL, tail and brake light is one bulb. When I replace the bulb, it stays lit then it fades out in seconds. It is brand new bulb. Do I need bulb grease or di-electric grease?
Swap the bulb with the one from the other side. If the problem moves it’s the bulb. If it doesn’t move you’ve probably got a bad socket that loses contact as it heats.
I’m curious. What do you think the grease will do?
Di-electric will hot help here. It generally can help prevent a problem, but it usually will not fix one.
I have this crazy idea it will help the electrical conduction of the bulb to the socket. This bulb was just replaced and other bulb I had no problems with ever (no problems with the socket). I will swap the bulb from the other side and see what happens. The old bulb had that yellow grease on the base.
A dielectric material is an insulator and would inhibit electricity conduction. There are probably greases that are condcutive that you could use, but that is probably not your problem.
Perform the test that JayWB suggested. If it is in the wiring, inspect the insde of the bulb connector. Is the metal conductor discolored? If so, you might buff it up with a little emery paper and try the bulb again. Also check the wire connections to the bulb connector if they are separate from the bulb electrodes.
Dielectric grease is used to prevent moisture and other corrosives from getting to the electrical contacts. The grease is designed NOT to conduct electricity, causing shorts. IF YOU USE A CONDUCTIVE GREASE IN THE SOCKET, YOU’LL CAUSE ALL KINDS OF ELECTRICAL PROBLEMS WITH CONSTANT SHORTS.
PS Bulb grease IS a dielectric grease.
Sorry can’t help myself blinker fluid? 
Seriously you probably need to replace the socket.