There is a switch. I think on most C/K 1500/2500 it is on the brake pedal arm or the arm hits it. It is $5-$10; you might take ALL your truck data to the auto parts store, buy a new switch, then look for the same thing around the brake arm or under the hood.
There's a fuse. Find the fusebox and look for "brake". The Owner's Manual may have clues.
Fuses usually blow for a reason. Some bulb-faults can blow a fuse. Change the brake lamp bulbs; on a vehicle this old it is time to do that. Open tailgate, there's two (rusted) Phillips screws into the taillight lens. Unscrew, the lens un-hooks on the other side. Flat rubbery thing with connector and 3 lumps. Unhook connector latch and carefully pull out. Use 1/4 nutdriver to remove 2 screws in rubbery thing. Three bulbs: they just pull out but won't want to come easy. IIRC bottom is backup and the top one is brake.
Look at the wires, because if it is not switch and not a bulb-fault, then as TBAS says it is probably wires, pinched or broken, from tail to switch to fusebox.