HERE is how that works
Ma uses the starter relay to relieve the key switch from the high current of the starter solenoid, as well as incorporating the neutral start safety into the mix
The two small "flag" push on terminals are the relay coil. The yellow, connected to one, is the "start" voltage coming from the key switch when you twist the key to "start." But the second terminal on the relay is to ground the relay coil. That wire goes down the firewall and connects to the center terminal on the neutral switch, which has 3 terminals. the outer two are for reverse lights.
SO TAKE a light or meter, and back probe the yellow wire. See if you have power when you twist the key to start
If so, try wiggling the shifter from park to neutral and back while holding the key to start. Any click, noise shows an attempt to crank. Either the linkage is out of adjustment, the switch is worn, maybe the electrical connector is loose.
If that does nothing, remove the dark wire from the relay --the one going down to the transmission--and use an alligator clip jumper to ground that relay terminal. BE CAREFUL You just bypassed the neutral safety. Making sure the lever is in park, try to crank the engine
This is a simple circuit. Power comes to the relay coil on the yellow, through the coil, and down to the neutral safety switch where it is grounded in park or neutral