Docs. First, the jumper needs to be super short because it will act as an antenna and pick up RF interference. Since this is a low level signal, everything will get amplified by the amplifier.
Secondly, the whole exercise here it to bring a known good audio signal to the input of the side that is not working. Hopefully, it will tell you if the amp is blown. If the amp is good and it's starved for an input signal, bringing the signal from the other side should accomplish that. With the signal being shared, reduced impedance could load down the other side so distortion and low output is not uncommon. Again, we are just trying to test the amps ability to amplify a signal. Keep in mind that the amp input signal at the pins is AFTER all signal processing. Do you see what you are doing wrong now?
By turning the balance knob ALL THE WAY to the bad side, you introduced another factor. If the issue is before the amp, say in the pre-amp, you just turned the signal to the possible dead side. So if the preamp is defective, and you turn the signal all the way to the bad side......... there is no way for the amp to amplify a dead signal. Try this again with the balance at neutral or at the good side and retry.
If all you got is a voltmeter, I'm not sure you have enough equipment to test and determine the problem. On the other hand, if you have a service diagram with V-R test point specs, then you CAN indeed test and determine whether the circuits are working as they should. Basically, as you traverse the circuit diagram, there will be voltage and resistance readings at various critical locations including almost all IC pins. If you have an audio signal generator, you can inject an audio signal at the amp to see if it will amplify the signal. If you have a signal tracer, you can test backwards from the amp through the circuit until you find a break in the signal. Anyhow, sorry but maybe someone else can think of a more simplified manner to test the amp for you.
As for the amp module being hard to extract -- that probably is not unusual. Most amps are in pretty obscure and hard to service locations. After all, amp failure is not that common of a malady. Also if you do need to remove the amp module, and you decide to do it yourself, always, always secure it properly to the heatsink with appropriate heatsink grease. Then solder it in last. That accomplishes 2 things. First, it always helps to have a little heatsinking to protect the chip. Second, once the chip is soldered in, it's almost impossible to fasten it down so it will sit flat against the heatsink. A GF-9797 is worth fixing. If you no longer want it, ship it to me.