Interesting that it would restart right away.
I'm guessing that this system works similar to the V6 in that the ECM turns on the relay, which runs the pump.
I'm also guessing that the oil pressure sender supplies a backup to the ecm/relay circuit.
Based upon those suppositions, I would disconnect the oil sender, and see if it starts and runs at all.
If it does, I would reconnect the oil sender and unplug the fuel pump relay and see if it still cranks and runs.
You might be able to draw conclusions from the results.
The fact that it restarted after turning the key off and then on (and start) also leads me to believe that if it died again, you might be able to leave it in gear and just cycle the key. The forward momentum would serve to start the engine.
If it requires an actual switch to the start position, it might indicate a failure in one of the ignition circuits. (Again, based upon the premise that the V6 ICM has different start and run circuits. I'm guessing that the Duke ICM is similar.)
Of course, it's not a bad idea to check the fuel pump and hose. But stuff is always easier to fix if it will stay "broke".
Working in telecommunications, I always hated those mysterious "miracle fixes". They always seemed to "unfix" themselves at an inopportune time. Usually at 3:00 AM, on a week when I was on call.