First thing that needs to be asked is if you used the correct switch. There was a 2 speed and optional 3 speed wipers. You need the correct switch.
Assuming you have the correct switch, it's usually the park switch inside the wiper motor itself that isn't adjusted correctly or not working correctly that causes that. The dash switch actually reverses the motor and the switch inside the wiper motor lets it park and shut off. There's some switch and motor tests in the FSM that you should try. If you don't have one, download one here:
MyMopar