Honda EU3000is will not start

I still think you will find that the ICM ignition module is the problem. Diagram shows that there are two ways to kill the spark--by the ignition key switch grounding the spark, or the yellow wire from the low oil device grounding the spark. Both cause the coil black wire to go to O ohms stopping the engine. Igniton switch is by direct connection and low oil circuit is by an internal transistor or diode juction inside the ignition module.
Remember when they say "module" it nearly always involves solid state devices. I think the difference between 1 ohm coil resistance and .2 ohm is if the engine will run or not. My thoughts.