The click you are hearing could be a bad relay, but it is hard to say. If you remove either the tweeter or the small plastic panel (depending on your car's options) at the front corner of the window glass on the door, you will see a three wire rectangular connector. If you have access to a multimeter, you could disconnect this connector and test the wires for voltage by connecting the test leads to the car-side of the connector and activating the mirror switch. If you have voltage, the motor(s) in your mirror are likely seized. If you do not have voltage, the relay in the circuit is probably damaged.
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