Patio, I have good news.
I took the module to my Uncle Bill. He actually succeeded in fixing the broken right audio output. (No harm was done to the unit.) The right audio jack's problem was caused by a solder joint that wasn't connected properly. (Somebody must have done work on it earlier.) On top of that, the board wasn't seated on the bottom cover correctly and the CR2032 battery was leaking. It has a new battery now, the main board is properly grounded, and the solder issue is gone. My uncle also verified that the jacks were working completely when he tested the output and input jacks with a multimeter. None of the jacks were intermittent. The issue with the leaking battery prompted me to check out the battery in my first Roland SC-55, and I found out that it was just barely starting to leak. It's a good thing the package came with two CR2032 batteries. My uncle's notice of the battery issue helped to save both modules. The only thing left is to check my Roland SC-88Pro to make sure it isn't having the same battery problem. (I hope it is not.)