1990 Sierra

For the tail lamps, the brown wire is voltage, goes hot when you turn on the headlamp switch. Use a digital multimeter between brown wire and vehicle ground/metal part. You either have to backprobe the brown wire connector or penetrate the insulation on the brown wire, headlamp switch on, What is the reading?

Also, black wire is ground, if there is much voltage on the black wire, the ground is faulty.