Without doing any research, just a quick thought. Looking back at photos of your wiper motor, you have the washer pump integrated into the wiper motor.
There are two sets of wires going to the motor. One drives the wiper motor and one energizes a solenoid for the washer pump. I would try pulling each set of wires off individually to see which is causing the buzzing. I am kind of thinking it's the two wires that energize the solenoid. If that's the case, I wonder if the wash button on the wiper switch is stuck.
In the meantime, I would make sure you keep the battery disconnected until this problem is resolved. Actually a good idea anyway for now.