Sounds a whole lot like a bad ground. IMHO, the brake lights are missing their ground, and thus using what is called a "floating" ground thru the other light circuits lighting them up in the process.
I am not very knowledgeable in the post 70's truck electrical , but I would check the ground studs and wires for the rear light assemblies. Especially the brake circuits, also check the bulbs and sockets for corrosion.
I do not know if Ford added any switches or relays to those "new fangled" trucks that could go bad and cause these problems

Sparky