Sounds like a leaking booster. You can usually hear it hissing thru the firewall opening. Rust inside the brake hydraulics would cause sticking calipers and MC and leaks.

One way to test the booster is to turn off the engine, wait 20 sec, and see if you still get assist. The booster should store vacuum (via check valve) to allow one braking cycle after the engine dies, as a safety feature. Of course, the check valve must also work.

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1984 & 1985 CA 300D's
1964 & 65 Mopar's - Valiant, Dart, Newport
1996 & 2002 Chrysler minivans