It's good that you've managed to isolate the problem to the Joy-Con specifically. The damage you've found on the ribbon cable (from my understanding) is also a valuable clue that helps validate the likely need for a replacement of the Joy-Con rail, which that same cable is a part of.
The first step I'd take is cleaning the connector of the rail with contact cleaner like IPA and a swab or similar. Do this while the Joy-Con is off and see if the problem persists. This helps ensure that your problem is not caused by debris, which would necessitate the replacement of any components. Confirm that the ribbon cable is properly seated to rule out that being a potential cause as well. The next step I'd take -if possible- would be to get a Joy-Con of the same side and swap the rails to determine whether or not that is the true source of the malfunction. If the Joy-Con works correctly with the alternate rail, then you can be fairly certain that's the part you'll need to replace. If it does not work correctly even then, your issue is potentially one that involves the motherboard. Leave that possibility aside unless necessary, though.
Be careful with the last troubleshooting step, as the ribbon cables are sensitive- especially the top one.
It's good that you've managed to isolate the problem to the Joy-Con specifically. The damage you've found on the ribbon cable (from my understanding) is also a valuable clue that helps validate the likely need for a replacement of the Joy-Con rail, which that same cable is a part of.
The first step I'd take is cleaning the connector of the rail with contact cleaner like IPA and a swab or similar. Do this while the Joy-Con is off and see if the problem persists. This helps ensure that your problem is not caused by debris, which would necessitate the replacement of any components. Confirm that the ribbon cable is properly seated to rule out that being a potential cause as well. The next step I'd take -if possible- would be to get a Joy-Con of the same side and swap the rails to determine whether or not that is the true source of the malfunction. If the Joy-Con works correctly with the alternate rail, then you can be fairly certain that's the part you'll need to replace. If it does not work correctly even then, your issue is potentially one that involves the motherboard. Leave that possibility aside unless necessary, though.
Be careful with the last troubleshooting step, as the ribbon cables are sensitive- especially the top one.