The right-hand meter is also used for the battery test function, so I would start by checking the battery test switch and its wiring. The switch has a changeover action; at rest, the positive terminal of the meter is connected to the monitoring preamp but when depressed, it is connected via a preset variable resistor in series with a fixed resistor to the positive supply.
There is a PDF circuit diagram
here although it's all cut up and awkward to read on screen; might be OK printed out, though. It also includes pictures of the various boards, which should help you identify what is where.
If you have some sacrificial tape, does the noise on the left channel get recorded?