Why would the engine quit when turning on the R magneto after an overhaul?
There's 3 potential problems. Magnetos are very simple in how they operate, and the system basically runs on 3 things that can be easily tested.


Spark plugs, engines can die because of 1 bad spark plug, I've had engines become extremely rough and die within 5-10 seconds when checking R/L because of 1 plug with a piece of lead shorting the electrode.
Magneto itself. I highly suggest against opening up and replacing anything in high-time magnetos in the field for multiple reasons. In case of Slicks, the magneto components are designed to wear at an even rate i.e replacing point contacts or a capacitor is not a wise decision for maintenance or for cost-effectiveness over time. An overhauled 4300 series magneto is ~600 dollars, the labor and parts for internal parts reaches that quickly for a substandard magneto as the finished product. I can't speak as much on Bendix but magnetos are a mix of old, complicated, and mechanical that means high wear and high chance for improper reassembly. In this case I assume your O-360 is running 437X Slicks.
Wiring in the ignition switch. You cannot improperly wire a magneto(as far as the operation of the magneto is concerned on a 360, any absence of wires won't stop the operation), and personally this is the least likely of the 3 especially if you didn't touch the ignition. Improper wiring of the backend or improper switch installation could cause this, but again I would highly advise checking the 2 before.


I know this is long past a point of help but I think it helps to explain for anyone else interested