[tsubaki]

Here is a way to rule out it being part of the wire harness or if it's a problem at the engine, if you know how to jump the starter solenoid.
One problem in doing this, there is no way to shut the engine down being you have a primer system and not the butterfly choke. You will have to unplug the gas hose and let it run out of fuel.
Run a water hose to the engine, just like you are confident it's gonna start and run.
Unplug the big red harness at the engine, manually prime the carbs (instructions on the air silencer), jump the starter solenoid to see if it wants to fire.