You will need to replace the wiper motor to repair the problem. The park circuit of the wipers in contained in the motor itself.
I have found that the wiper motors in the aftermarket will not function properly in these trucks.
You will need to get the replacement assembly right from your local Dodge dealer. Be sure that when you get the replacement assembly that they also sell you the replacement wiring harness. The new motor will not plug into the original connector(go figure)..
Please ask me any questions that you may have...Thanks, Josh