The Amiga RCA jacks have built in switches so that if only one RCA cable is plugged in (for mono systems) then the other audio channel is connected so that both of the output channels are joined together at the single RCA output.
If two RCA plugs are connected, the left and right outputs are seperated.
Your problem sounds like one of the audio output stages is dead. Quite likely to be the 22µF electrolytic capacitors leaking corrosive electrolyte onto the board.
I've written a complete guide on this as well as an audio test utility to help testing and repair:
http://amiga.serveftp.net/audio_repair.htmlUnfortunately my webserver is offline right now due to my ISP being a giant arse, but should hepefully be back in a day or two.
Perhaps Google or WayBackMachine might have cached the page so you might be able to see it in the meantime.
