An oscilloscope is the ideal tool for tracing signals but the fact that the voltages are almost identical on both channels makes me think the problem is an open circuit capacitor. Usually, although not conclusively, a dead channel would show some significant DC differences so my guess is the problem lies with a component that doesn't conduct DC at all and hence isn't upsetting the voltages you measure. The component meeting that criteria is a capacitor, I'm still thinking the output capacitor is at fault. Regardless of whether that is the culprit, after all those years it will have deteriorated considerably and for the low cost of replacements it would be a good idea to replace it, and all the other electrolytic capacitors with new ones.
Try another test please, select a quiet input, record deck without a record for example and using a screwdriver as a probe, place your finger on the screwdriver shaft and touch its tip on points 137 then 149. Hopefully you will hear a hum from the working channel but not from the faulty one. The methodology is that your body will be picking up electrical signals from nearby sources, primarily 50Hz or 60Hz ones and you are using the screwdriver as a signal injector to feed it into the amplifier inputs. It is safe but just to be sure, don't touch anything else at the same time. Let us know if you get a big fat hum from one or both loudspeakers please.
Incidentally, that scope from Amazon is of limited use because of its low bandwidth. It will just about do audio tracing but useless for RF or digital signals.
Brian.