The brake lights on 1997 Ford Escort Wagon stay on after the car is turned off.
You probably have a short to ground in the circuit or the “normally off” brake light switch is stuck in the “on” position.
Brake light circuits are always “hot”, even when the car is off. They’re designed this way for safety. If the circuit has found a ground the lights will stay on even with the key out.
I would bet that the brake light switch is stuck in the on position. If this is like my Ford Tempo or my Ford Windstar, this is an easy no tool repair. A new switch is about $15 at an auto parts store. It clips into place under the dash where it is activated by the brake pedal lever. The wiring connector just plugs in.