NO THAT IS NOT correct SOL does not go in series with the neutral switch, and does not go to solenoid
The circuit path from the ignition switch S wire (OEM YELLOW) is direct to the start relay coil, through the coil out on the NSS wire, down to the transmission, and to the center terminal of the NSS. If a stick car, ground the second coil terminal or run it through the clutch switch which then grounds it
The RELAY then activates the solenoid by way of the "big square" terminal on the start relay, no. 12 or 10 from there to the starter solenoid
So you are firing a ford solenoid with the Mopar relay? I assume you have the Ford solenoid in the big starter wire and using a smaller wire from the alternator?
So first you need to see if the Mopar relay is working. It sounds as if it should. Put a light or meter on the "start" wire from the key there at the Mopar relay and it should power up in "start." Then move to the large "square" terminal on the relay which formerly went to the Mopar starter solenoid. That should power up as well in crank.
That square terminal should feed back to your Ford relay, which must be grounded, and should hook to the small terminal marked "S" on the Ford. If the Ford has a second small terminal, it was used for ballast bypass and will not be used.
If that is what you are doing, you should be able to hear the Ford relay fire. You should have the Mopar solenoid terminal jumpered to the main terminal, as the Ford solenoid will power up the entire thing.
if you refer to your own post, the small had drawn diagram, it shows (in green) the feed I'm talking about.
It also shows the jumper at the starter
Other than than, "I can't see" what you see, and obviously this is not factory. So it's a matter of following the power and see what is getting power. If you have someone to help, or can make an alligator clip jumper, you can manually power the small terminal at the start relay. You should hear it click. You can use a light/ meter to see if the "square screw" is then powered, or you should hear the Ford solenoid engage.