The full voltage to start your engine is supplied by a wire that runs from your starter solenoid to the coil. That supply would appear to be functioning properly from your description. You didn't mention what year your Scout is, for shame for shame. The voltage to keep your engine running is either supplied by an ugly, cloth insulated resistor wire or by a standard awg wire that is interrupted by a ceramic ballast resistor. Which is it? Only you know that. Either way, the wire in question will be part of the loom that goes through the main bulkhead connector on the passenger side of the firewall. If you know anything about scouts, then you know those bhc's are the single most problematic pieces of shit on the entire rig.
To rule out this being anything other than a voltage supply issue, you can jump a wire directly from the + terminal of your battery to the + side of the coil as a temporary hotwire. If the engine continues to run, you know for certain the problem is in the run circuit that supplies b+ voltage to your coil. Don't run the engine too long this way as it will damage your coil and/or points.