Well it sounds like you have spent a fair amount of time and money on the troubles without much success. If you plan on keeping this vehicle I suggest you purchase the factory service manual for it. It will really help you understand how things are connected for the wiring and the other mechanical systems of the vehicle. It is money well spent if you want to work on things yourself. Having a test meter is also a good investment.
I agree with @Tester, the wiper trouble is most likely with the BCM module. Using the service manual and meter you could verify that the wiring to the module is okay first before committing to purchasing one.
I assume you have made sure that the right side bulb is still good and isn’t blown out. It sounds like there is a faulty connection causing the trouble.