Bad switch or bad motor. There is a board in the motor that controls parking the wipers. If it goes bad it can cause what you are experiencing.
You need to locat a diagram and make sure the switch is working properly. You dont want to buy a motor and find out it is something else
Yes you can. Wire the switch in where the circuit breaker goes, just 2 leads to the switch with 1/4" male spade connectors on the ends will plug in the fuse block where the breaker goes. Include the breaker in one of the wires.