The brake switch comes on when you have the ignition in-between run and start for the bulb test, parking brake applied, or when the combination valve is thrown for whatever reason. It's possible the switch got stuck on your parking brake. Do you even use the parking brake? Did you try raising and cycling the foot lever by hand with the release handle pulled?
There's a tan with white stripe wire going to all 3 of these what sets off your lamp- so either you've got a nicked tan/white wire that's being grounded for whatever reason, or something is really amiss with one of these. Could it be the ignition switch at the base of the steering column (tan/white wire there on the switch plug)? Doubtful, but not out of the realm of reality. Maybe it's the switch on the parking brake. Look for a tan/white wire pigtail going to it on your parking brake. It's a normally closed switch that's held open by the position of the foot lever. Maybe the copper strap got hosed and won't open for some reason. It bolts (and grounds) to the parking brake assembly and is held open when the parking brake is fully released, which keeps it from grounding, until you press the foot lever and allow the flat spring switch to close. Kinda like a thick reed switch. Unplug the pigtail, and test for the lamp again. If the light goes out, you're in the right place. If not, check something else. If it is the brake switch, you can get them new on ebay or Amazon for a few bucks. Shop around. GM p/n 1264464 or Standard DS-905.
7.95 with prime (free shipping).
If you can reach it, remove the plug on top of the combination brake valve on the inside of the frame. If your light goes out then, the switch has "tripped" for whatever reason or there's a renegade ground in that part of the circuit. If it's still on, then it's likely something else. That's a PITA because there's no good, easy way of resetting it if the switch is tripped. That button up front does NOTHING for that. You may be able to remove the plastic switch on the valve, and reaching in with a pick tool and moving the spool back to center. Much easier to do off the car.
If you work on your car, you should have a set of the CSMs. AKA Chassis Service Manuals. They're specific for your model and year. I never leave home without them. Worth their weight in gold.
There's very little the CSM does not cover.
BTW, here's an auction on ebay that has the complete set, including a couple of non-GM books, an 85 Chilton's manual and a 1985 Motor Vehicle ID number book. For that price, it's a great value considering what you get. Just the basic 2 manual set cost over $200 when you could still get them from GM. Like a dummy, I paid full ride from their printing place, but there was no ebay at the time and had no idea where I could have got them slightly used. The GM basic set on this one looks to be almost new. The only thing missing would be the 1985 Fisher Body manual, which has good info in it, but it's like an old, high school science book. Uses some pictures from the 60s...
This manual will save you money in repairs/service. This manual is published by GM.
www.ebay.com