Quick answer is any working two channel scope will be fine, all you need.
After confirming it is not the relay, use the scope when it is not working to see if that is the interruption point. If not and after careful board inspection, magnifying glass, having spent a few years as a bench tech, time is money, I would reflow each solder joint on the board, fixed many intermittent problems this way, often beats time spent tracking down a bad solder joint. I say this with experience using a good solder station, no bridges and overheating of components. Not at all comfortable giving advice to others without day to day practical experience but that is one approach. I doubt it is a component failure... transistor, capacitor, other, but could be, that is where 'freeze spray' often helps. I think it is a bad connection to board or bad solder joint, not unlikely to be one of the relays but they can be tested for continuity through their contacts. I've seen solder joints that look fine but aren't. Intermittents can be tough to find. You should obtain the schematic, the service manual will provide block diagram and board layout, very helpful. That amplifier has a very good reputation.