Time to test the brake warning circuit and switch.
The brake warning lamp in the dash has two wires, one (dark blue) provides + voltage. The other (black) goes through bulkhead connecter terminal #12, to a switch below the master cylinder, in the engine compartment, and gets ground to illuminate the lamp.
There may be a short grounding this (black) wire, the safety switch is faulty, or something amiss in the proportioning valve. Try disconnecting the wire going to the switch, and see if the lamp goes out. If not, the switch may be fine, and you gotta look deeper.
Back in the 1980s, I drove a 1970 barracuda with a failing master cylinder for almost a year. The brake warning lamp would frequently come on. I could milk function from the master cylinder by pumping the brakes. In stop-n-go traffic, the lamp was on for long periods of time. At one point, the lamp stayed on. Even after repairing the master cylinder. After some troubleshooting, I found the black wire got too hot, (presumably) because the lamp was on for long periods, and the black wire melted its insulation and melted another wire to ground. The long and short of it is, I had to repair the wiring harness coming from the fuse bulkhead up to the instrument cluster to resolve that problem.