[Rich Biebel]

Most later 4KY's have the coil mounted under the blower/flywheel.
The coil wire is part of the coil and it is a magneto type ignition.
The coil wire is at a very sharp angle as it routes to the spark plug.
The vibration of the engine and the bad angle of the wire often causes the wire to fail. It is a carbon core type wire and you lose spark as the unit gets hot......
Possibly your problem....

Fuel pumps are a piston design and even though you see fuel coming out cold.....it could still be your issue. If it was never changed and the unit has some hours on it.....it may be your problem....

The solinoid on the carbs fuel bowl energizes with the pump and allows fuel to flow. If has a ground wire and a B+. They don't fail often but do get stuck from a unit that sat with fuel in it....