OK, just took a look.
If the engine cranks, the lanyard & stop switches are probably fine. You could verify this by holding in the stop switch & seeing if it will crank, & pull off the lanyard & see if it will crank. If it won't with either removed, those should be fine.
next, make sure the black wire from the MPEM is grounded & that the red/white has a constant 12V. then check to see if the black/white is connected to the wire that comes from the starter button. This wire gets a ground when you hit the start button & wakes up the MPEM. If you tap the start button, the mpem should energize you should be able to hear the relay turn off power after 30 seconds of tapping the start button & the purple wire should have 12V during that time.
The black/yel should see a ground while the lanyard is in place. this wire should plug into a black/white This is the same ground loop that goes through the lanyard & stop button, & also provides a ground to the start button & loops back to the start solenoid.
The yellow/red that goes to the solenoid should also have 12V on it at all times.
If all that checks out, & it still only has spark when the black/red is disconnected from the coil, I would lean towards a bad MPEM, but make sure everything else checks out first. There is a also a test procedure for the MPEM when everything is unplugged from it.