Better than on the way to the wedding...
That bundle of wire is the control signals. If you can extend that cable then you will not need to move the generator. However, unknown is if the signal voltage has too much of a drop in voltage between the two you may run into issues. Are they 24v ac, 5v DC or other voltages? Perhaps a call to Kohler is needed. Any changes may void the Kohler warranty. The electrical code is low voltage cables and wires cannot be run in the same conduit as electrical power. You may be in the same situation.
At one time
www.Gates.com had a chart of vehicles with and without interference engines. They don't seem to have it anymore. It used to be good place to search when looking to buy a used vehicle.