I'm having a very serious problem with an ABS equipped 97 F-150. Under any pressure and at random times the brake pedal will push back. It has already caused a rear end collision at my "fault". The truck has about 270K miles on it and the truck is spitting out a Wheel Speed Sensor code for the right front.

When this occurs do the brakes fail and is this why you had a rear end into someone else? Or did the brakes lock up causing someone to rear end you?
Could be an obstruction or a pinched or crimped brake line. Loss of vacuum boost, stuck brake caliper or stuck inlet (isolation) valve or a brake anti-lock sensor. Whal is the Diagnoistic Trouble Code? Take it to a shop that does ABS work. Brakes are too important to take a chance.