Sounds like you have a problem with your brake light switch under the dash, mounted on your brake pedal metal arm assembly. I know if I get my head down near the brake pedal and push the pedal with my hand I can hear a loud click noise when the brake lights come on. I'm not a mechanic, but I've wondered if the brake fluid level is down in the master cylinder, does the brake pedal drop enough for the brake light switch to turn on the brake lights ?
They are supposed to turn on when the engine is started and the emergency brake is released , at least that is the way it is on my 1995 Ford Explorer
engage the parking brake , or shut the engine off
On my 1996 Explorer, when you set the park brake, the DRL lights shut off.
On a 1997 Ford Explorer : The push button switch to turn on and off the fog lights is in ( the center stack of the dash , to the right of the radio )
If the Explorer is running engaging the parking brake is supposed to turn the daytime running lights off , otherwise the daytime running lights are supposed to shut off when the engine is shut off . I have a 2004, Eddie Bauer Explorer. On the light switch itself, there is a selection to turn on or off the day lights, as well as the extended, courtesy lights after ignition is turned off.
The brake lights won't turn off because the brake light switch on the pedestal of the brake pedal needs to be replaced.
Try pushing your turn signal lever forward , that's what I do to turn on my high beam headlights on my 1995 Ford Explorer
Brake light switch is broken or needs adjustment.
On a 2002 Ford Explorer : On the headlight switch , select automatic , park lights, or low beam headlights and pull the headlight switch out towards you to turn the fog lights on ( push the switch in again to turn the fog lights off )
I dont know because i dont have a FORD Check your brake light switch on the back of your brake pedal for adjustment.
I am not sure on a ford but i had about the same problem on a GM car i had and it was the turn signal switch i replaced it and all the brake lights worked fine you might try that
Most likely turn signal flasher