[Richard]

First English is a second language for this redneck so I often need translation. Have you applied 12v directly to the trigger terminal on the start solenoid in your last pic? Does the engine turn over and or crank? The answer will tell us a lot. Your comment “has no continuity” sort of is unclear to me. You should have 12v on the wire when the start circuit is engaged.

Regardless replace that solenoid because it is a known failure. I think its a cole hersee intermittent duty.

I dont know if you can see the fuel shutoff solenoid. If so does it open when the engine is ON?