Start with checking the spark, should get minimum 1/4" spark to ground at the plug end of each wire. Not at the cap, but at each plug.
If good, check the fuel delivery to the carb. With the engine off, fuel valve on, have a clean glass ready, remove the drain plug from the carb, catch the flow. It should have a full flow, slowing as the bowl empties, but not slowing to a drip or stopping. If it does slow or stop, trace the problem back toward the tank. There may be a screen in the inlet fitting of the carb, and one in the tank. Look at what was caught, if cloudy it is water contaminated. If dirty or rusty the tank will need to come off and be rinsed and dumped out. If severely rusted it may need to be replaced. Whatever is in the glass will also be in the carb. It may need to be eased apart and cleaned out.
But the best diagnosis is done when it is failing. Be ready to check the spark and fuel delivery immediately when it fails.
A properly operating coil will be about the same temperature as the surrounding components. If too hot to hold, it is getting too hot.
Be sure the gas cap is vented. Try opening it when it fails.
Be sure the fuel line is routed as far from the exhaust manifold as practical. The original fuel line would have been steel. If a copper line has been used, it is more conductive than steel and promotes vapor lock.
If there is an inline fuel filter, that can be too restrictive for a gravity system. With a clean tank, the original screen and separator are sufficient.