Pulsating brake pedal

Time to take it apart and see what has failed. Do you feel the pulsing more in the steering wheel (side-side shake or pulsing) or more through the seat and floor? Steering wheel would be more likely the front brakes while seat/floor are more likely the rears. Grabbing and pedal pulse can be created by multiple problems, with drum breaks it can be leaky wheel cylinder, rusted drums (especially if it has sat for a while) or cracked or bent drums.
In the front a cracked rotor or one that has been damaged from impact.
It is also possible it is something like a bad U-Joint that binds under braking but those are rare.
If you drive slow and hold the pedal down do you hear or feel the truck jerk as the tires rotate? Do you feel the pedal issue only at high speed?

Have the front rotors machined and if they are too thin afterward, replace them.
By the way, there is no 1981 Ford Explorer. The Ford Explorer was introduced in 1990. There also is no such thing as a 0.5l engine.