Clarification. There is a motor and a transmission. The transmission is at the end of the motor housing. The linkage assembly, the motor is mounted on, is often included as the transmission in discussions.
There is a connector from the motor to the wire harness right next to the motor that could be allowing water to create a connection that is loose.
I just had a similair problem where the intermitant mode would only work intermitantly! I ended up taking the assembly out, removing the cover over the transmission portion of the motor. The cover has the wires attached. Inside are three "arms" that are conncector springs on the cover attached to the wires. They ride on a ringed disk to transfer the ground and power to the motor. Greese is plentiful and should be redistributed. One of the springs was "unsprung". I think they loose their "spring" over time. I simply bent it to increase the contact force. Don't need to go overboard, just get it to be a little more bent then the others. Now everthing works. There was a rubbery paint over the motor assembly from the factory to help seal the cover in additon to the gasket. You may want to paint it after assembly.
BTW, you may want to check the control box. It is located under the dash with velcro on the left side of the steering wheel. You can remove the connectors on both sides and plug the two together, eliminating the box. If everything else is good, you will have only low and high speeds for the wipers. This is a way around a failed control box.