I think the click you are hearing is a relay. The switch connects/disconnects a low amperage wire that powers a relay coil, in turn making/breaking a higher amperage connection to the motor. Like a power window motor, the switch and relay swap the motor + and - terminals to make it run forward or reverse. I'd be looking at the wiring to the motor from the relay.

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1986 560SL
2002 Toyota Camry
1993 Lexus