Sorry there are no " vacuum " lines on that carburetor.-----The wee hose comes from the primer valve.----Puts fuel into the motor for starting when cold.
That is a cut off switch and stops spark to one cylinder during high vacuum.----Has nothing to do with a fuel pump diaphragm either.----Find the wiring diagram and get this corrected.
It was when it left the factory.-----Now after possibly 4 owners you need to inspect the motor.----Take it for an on the water test run.-----Install a new water pump impeller if you do buy it.
Did the new powerpack help ?-------Post the results of a compression test.------Have you replaced water pump impeller.?----Motor might be going into S.L.O.W.
You could start with doing ( learn perhaps ) some trouble shooting.-----Or try a new stator.----If you are wrong you will have a $300 spare part on hand.
Kill switch wires should be connected to STOP the motor.-----If those are connected together there will be no spark.-----Wiring can be confusing I say.
???----Post #1 clearly shows the shift interlock pieces are missing !!!----Likely removed because motor was not running properly.----People do that as a last resort to keep a motor from going to the " fix it shop " and getting a diagnosis.