2001 Chevy Express Brake lights don't work when headlights

You either installed the wrong bulbs, the socket is no good or the ground for the light socket is not there. Why they dont work when the lights are on due to back feeding because of no ground. Make sure you are using a 2 filament light bulb, sometimes people mistakenly install a one filament bulb and this too can cause this to happen. If e brake does not hold its almost always caused by bad e brake shoes. It is usually necessary to replace rear rotors and e brake shoes with the hardware and I find almost always the adjuster is frozen.