sounds like it is getting stuck trying to go into the "sleep" position. I don't know if there is a relay that is part of the wiring but that could be buzzing. I would suspect the problem is mechanical. Maybe something is loose or bushing worn or broken so it is not functioning correctly and the relay is not getting a proper signal to shut off the power. Just a guess on my part.
They might not be parking all the way when parked position . pull the wiper arms down closer to the bottom of the windshield and see if the buzzing stops. If it does you might have to take off the wiper arms and re position them
Take off both wiper blade arms or angel them out where they're not touching the windshield. Turn the switch off and see if it quits buzzing. If it does you might have to reposition the wiper arms when putting them back on. They might be going down too far towards the bottom of the windshield and not letting them shut off. If this doesn't work i'd say it's a bad switch