pedal vibrates when brakes are applied, '91 Imperial

When I press on the break pedal, stopped or while moving, there is a buzzing sound and the pedal vibrates. Does anyone know what is causing this?

If the car has ABS it may be in relation to that.

This happens almost every time I press on the break. I don't believe it is an abs type of sound.

I have the same issue. This is the ABS module. Not sure why or what, but it is common.