I've replaced the bulb to no effect. I've even taken the brake/reverse light housing from the affected side and plugged it into the wires for the other side -works great! Seems clear that the problem's electrical, how can I further troubleshoot/fix this? Thanks for any tips.

 

only one side works? or neither? if both - check your fuse

 

Yes, only one reverse light works, the other doesn't. Both brake lights work.