1994 Chevy Cavalier Brake lights?

Most common problems is bad grounds , find their ground wires in the trunk , make up a whole new ground connection run a proper o-ring wire connector to it and the brake light bulb ground wires, plus peel back the harness's and check for damaged or corroded or bear wires.

Also to try and balance the brake light system resistance I'd do the same thing run new bulbs and especially new grounds just be sure to use the same proper car wire and thickness etc.

Hope that helps and best of luck.By the way I'd be checking the wiring all throughout the brake system just in case a bad wire or loose connection etc.It not be a bad idea to go over all the electrical system from the fuse box , power junctions, battery, alternator , engine block ground posts one by one and clean them with a wire brush , sandpaper , a file and make sure no wiring is corroded going to them and if need be replace the wiring.

it could be a fuse or a brake light switch or a broken wire, check the fuse first you should be able to replace it your self. you might have to take it to a garage for the switch or wire

Brake light switch.

is it the middle one? if so, take the disguise away and the blown bulb besides. in spite of if that is one on the aspects, see in the experience that your vehicle's tailights have screws on the exterior, in any different case take the panels from interior the trunk out and get to the sunshine.