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Yes, that is the starter thermal switch that gave the Army fits very early in the FMTV life cycle. No promises, but that switch is as you say "likely inop". No promises, though. Next, if it were me, I would follow the "won't crank" troubleshooting tree in the TM.
Check to see if the thermal switch is bypassed on the starter, if not, bypass it. Connect two small white wires together that lead to a device on the starter not related to the solenoid. Disconnect battery before doing this. If that does not help, wiggle the relays in the Power Distribution...