This was done with the same amp and amp settings and with the same cord. I just simply switched the cord back and forth between the outputs . . . .
First of all, you shouldn't be using the same cord with the two different outputs - one is wired for a stereo plug (tip, sleeve, and ring), the other for a mono plug (tip and sleeve). I don't know for certain, but that probably has an effect on what's coming out of the amp. I'd try it again using a stereo cord for the Rick-O-Sound output and a mono cord for the mono output.
See pages 5-6: http://www.rickenbacker.com/pdfs/manual.pdf
The other part of this equation is the amp - with ROS you need to be using either a 2-channel amp, or two amps, or a stereo amp. Remember also that when using the ROS, the bridge amp/pickup volume will stay pretty constant, and the fifth control knob mostly just controls the neck amp/pickup volume. Finally, where is your p'up selector during this experiment, and how is your fifth knob set?
Please excuse any obvious comments if you knew all of this already.