1993 Chevrolet Silverado Tail lights

Your rear light assembly has a printed circuit board which distributes power to the bulbs. It is very common for them to go bad.

Remove the light assembly and you will see where one plug goes into the back of it. Using a test light, see if there is power to it when you press the brakes and turn on the signals. If there is, replace the printed circuit board that the plug goes into.