Assuming it has an inline Bosch injection pump, the only wiring the engine needs to run is the external solenoid that operates the injection pump on/off. It has one wire from the starter signal, and one wire from the IGN terminal on the ignition switch. All the rest of the wiring on the engine is gauges, there may be a grid heater that will have it's own controller, but that doesn't affect the injection pump or running after the first minutes in cold weather.
For the rest of the wiring, I'd suggest a power probe, and several alarms and lights with alligator clips to figure out the wiring that's hacked up.