I'm assuming that your deuce is a multifuel truck. Here are the wiring diagrams:
http://www.nf6x.net/greentruck/m44wiring/toc.html
Major players in the starting circuit are the ignition switch, the start button, a big relay in a round metal cannister, and the starter motor+solenoid.
The wiring diagram also shows a fuel pressure switch that I wasn't aware of. Ignition switch supplies power to the start button, the start button energizes the big relay, the big relay energizes the solenoid, and then the solenoid energizes the starter motor. I'm not sure why that fuel pressure switch is in there, and I don't remember it in any of my deuces... but I haven't had to debug any of their starting circuits, so I can't say with authority whether it's hiding in there somewhere.