Why would the left RCA ports on external speakers not work correctly?

see your bose service rep.

It sounds like the output amplifier on the left channel has gone south-kaput.

Bose has a proprietary wiring system like no other...Often they use a servo control method to feed power to their speakers those connections may be triggered by the servo sensor in the Bose amp or it may be something totally different...Often for Bose you cannot get a schematic nor service manual...Bose considers some of their ideas as 'Top Secret" and so you are forced to send it into a Bose authorized repair center for service and repair....You can even get sued for sharing certain technical information about some of their circuits.

I suggest looking up the model # of your Bose speakers and see if you can find a manual to make sure you are connecting them properly.