1991 Chevrolet S-10 Wiring

Just my opinion, I'd take one system at a time and check voltage and ground. The voltage wire for lower brake lites is yellow according to our info. So, have somebody step on the brake, while you check for voltage on that wire at the rear. Black wire is ground. Your lower brake lites are wired through the turn signal switch. You may also have to check voltage to and from brake switch.

The brown wire is voltage for your tail lamps, that voltage comes from headlamp switch. The ground wire is black.

The voltage for back-up lamp comes from either the neutral switch or backup lamp switch, depending on what type tranny, automatic or manual.