Starter relay question
The starter looks like the direct drive type. The large red cable goes from the battery positive to the solenoid terminal [normally off]. The other large solenoid terminal goes to the starter brushes. When the small terminal gets power from the ignition start terminal it closes the contacts, and electricity flows into the brushes. The armature quickly spins, forcing the bendix into the ring gear, and the engine turns over.
The remedy for neutral start can be done as stated by using a Mopar starter relay. Or, using a relay with two terminals to energize the relay coil. The second terminal would go to the neutral/park tranny switch. Or, you could mount the existing solenoid on a block of plastic/nylon to isolate it from ground. Then use the solenoid base as a terminal, and run that to the tranny switch.
More info is needed about the other wiring.