Originally Posted by Haggar
Those symptoms can also be caused by low brake fluid. Acceleration sloshes fluid away from the switch, braking sloshes it back.
I've seen this on sevreal vehicles before, but know nothing specific about broncos..
The E-brake is a cable driven system though unaffected by the fluid in the normal braking system. The only way fluid would cause the light to come on would be loss of pressure in the rear drum cylinder and the pads actually moving as a result to move the cable. It's very difficult for this to happen though really since the E-brake arm in the drum kicks the pads out when pulled and the spring on the outside of the drum pulls that level back out when released.