I have an '86 720 but I use an '84 Service Manual for my info. Not much changed from 84 to early '86.
OK, Follow your brake pedal up under the dash. It will have a rod connected to it that goes through the firewall and goes to the brake master cylinder. You will also see a bracket. The brake switch is mounted on the bracket. When you press the brake pedal, the little button on the brake switch is released. The photo below shows the switch pretty clearly. This is the first time I have looked at mine since I got the truck and I see someone has wadded up a little duct tape as a small pad between the pedal bar and the switch button. My finger is pointing at the duct tape and that is where the button is located. Anyway, check to see if the button is stuck. If the button doesn't pop out when you press the brake pedal, then the brake lights won't come on. If the switch itself is bad, then the truck brake lights don't get the connection to turn on. It's literally an on/off switch. The Service Manual calls it a STOP LAMP SWITCH.

Autozone or other parts supplier may carry an aftermarket switch. I have not checked much for availability.
Of course, if you have a short somewhere in the wiring of the switch or other place in the circuit, that could be the problem too. So before you go and spend money on a new brake switch, check to see if it is really bad or not.
I hope that helps. Let me know.

