The reason why I perform (and recommend) the "check for spark right at the plug" method, is because it doesn't matter if a spark signal that's able to be picked up by an inductive connection, is getting to the exterior, center connection, of the cap. What matters, (because it's what actually creates combustion) is that there is real spark, at a plug, that's sufficient to jump the plug gap. Even this test isn't perfect though, because a spark at a spark plug outside of the cylinder, doesn't mean there's enough spark energy to jump that gap under the squeeze of compression (hence why I recommend not using carbon core coil wires... too much resistance to current flow).

Regarding the carburetor that had the accelerator pump delivery nozzle fall out; I can see where this would cause poor acceleration, due to one pump delivering correctly, and the other pump just sort of flowing fuel down the carb throat, but I don't see how it could cause the engine to shut down and not restart. The accelerator pumps are only active when being triggered by movement of the accelerator pedal. When the pedal is held stationary, like at cruise speed, the pumps are not flowing any fuel.

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