Why won't my brake lights work on my 95 Chevy cheyenne?

Answer 1

Because something's wrong with them. It's either in the switch, the power supply, or the light assemblies themselves. Since they're both out, I'd look more at the switch, especially if your turn signals and four ways are still operational. You'll need to diagnose it... remove the brake light switch, check to see if there's continuity when it's depressed. If there is, you'll need to see if there's power going to the switch... if there is, then you're likely looking at a wiring fault somewhere between where it the brake light switch and the point where it splices into that circuit along with the turn signal wiring.