Hello! I've been following different threads for fixing the JA-S11G amplifier since i got my hand on one my self! I also had the same problem with only sound from one channel(Right) and as i was trying different things i noticed when i turned the balance all the way to the left i could hear a slight sound coming from the left channel, in my case this had to do with the "Monitor Switch" on the front panel, it has some kind of bad connection so when i worked it slightly up and down the sound would suddenly appear, and suddenly it was gone again. I would also think some of the others switches can have some malfunction/bad connection which causes problem with the output signal to the speaker relay on the back. Either way, this was after i replaced the two Darlington Power Packs(STK-0040, from Ebay) since the 24v- DC relay wouldn't switch over, and that would be the easiest way to try fix it, and it worked!!(shipping costs was over the actual price of the two Darlingtons), and then the next problem was sound coming only on one channel which in my case is the front panel switches, caused by being stored outside summer/winter(i would think?) for over almost 15 years! I hope this helps, it worked for me...
Edit: i used something called "Electronic cleaner", i just unscrewed the front panel, pushed the "clothing piece" aside and then applied some cleaning fluid as i rapidly pushed the switch up/down several times, i did this a couple of times and it's working much better but still the connection sometimes break, it may be possible to mod the switch in someway? With the help from a data sheet/schematic or something, or with the proper knowledge, i am not an engineer but it shouldn't be that big of a problem..