[Huskymaniac]

Also, I need to ask exactly what gets unplugged and what gets plugged when the engine is able to start. Does the engine start when the control module is unplugged and the resistor is plugged? Or, does the engine start when the resistor is unplugged and the control module is plugged? Or, does the engine start in either case? If the engine starts with either one unplugged is it true that when both are plugged then it does not start?

I am going to assume, for the time being, that the engine starts when the control module is unplugged and the resistor is plugged. I am assuming that there was a mistake at some point when it was said that the engine will start when the control module is plugged and the resistor is unplugged. Given that assumption, I would say that the resistor is probably fine and that the measurement of one ohm is probably correct. In fact, one ohm makes a lot of sense. That resistor forms a voltage divider with the pump when the pump is running. Electric motors tend to have a low resistance so the series resistor would have to be low as well. Therefore, I would conclude that the problem is the control module and not the resistor. Most likely, the final transistor in the circuit is blown (base and collector are shorted) and the control module is supplying 12 volts-ish, through the internal resistor, to the pump when it is plugged in. If that is true, the external resistor is probably getting very hot and the internal resistor in the control module is probably getting very hot.

Fly, can you either measure the voltage across the external resistor or, with a clamp-style current meter, measure the current through it? I would be curious to know how the voltage and/or current changes when the control module is plugged versus unplugged.