1988 Cadillac EL Dorado power brakes

It sounds like you have an early version of anti-lock brakes and not the common vacuum power booster. Most of those systems got their power assist from pressurized brake fluid. The switch you're referring to tells the pump when to build pressure in the system. That pressure bleeds off each time you apply the brakes. There is a common problem in the trucks where the pump runs continuously, overheats the driver circuit in the computer, which shorts and blows the fuse, or the pump just runs continuously with the ignition switch off until the battery runs dead. I don't recall ever hearing of a common problem on your car model, so the switch would be the thing to try first.