Brake light staying on
Mine came on when my master cylinder started to go bad. One of the seals was bad, so one side would work (front or rear) while the other side lost pressure.
When one side loses pressure, the high pressure side moves a plunger that closes off the side with the failure to prevent fluid loss and complete brake failure. When the plunger moves, the switch is opened, turning on the light. Once the switch is triggered, it has to be reset.
On mine, the electrical connector was the switch. It could be turned out by hand. Once the switch was out, the valve has to be centered. This can sometimes be done by pressing on the brake pedal REAL hard. More often than not though, you have to open up one of the bleeders on the side opposite of that that had the problem and bleed those brakes. This will create a pressure differential that will try to move the valve to the side that's open. Once the valve is centered, thread in the switch and the light should be out.
If the problem persists and isn't fix, it will just set the light again and you'll have to keep repeating this process. The brake light shouldn't come on on it's own, it's always indicative of a problem in the braking system.
These things are a pain sometimes, because the plunger tends to stick after 20-30+ years.
If that didn't make the light go out, then reach down and pull up on the parking brake pedal. If it goes out, then you need to mess with the parking brake mechanism.
The Ford shop manual says nothing to that effect and in fact describes it entirely differently, and the cross-sectional drawings don't depict such functionality being possible... the front & rear are two independent systems, a leak in one system will continue until the reservoir is empty (yes, the pressure differential will ultimately cause the dash light to be lit by the plunger in the switch being grounded, not opened) but, barring a problem on the other side, the other half will still work.
From the 1981 FoMoCo Light Truck Body/Chassis/Electrical shop manual (FPS 365-326-81-A):















