A Class C Motorhome Prep Chassis should have an extra fitting on the gas tank. Dedicated to the generator, it should extend about 3/4 of the way down into the tank. This is so you can run the generator till it runs out of gas and still have 1/4 tank to get your motorhome to a gas station.
It can be very difficult to access that fitting to add a hose for a generator if that was not done at the factory, before the House was built onto the Chassis.
You're right about fuel injection. The line FEEDING the fuel injectors is more pressure than the generator can accept. It'll force gas through the float valve and overflow the carburetor.
Fuel injection uses a Pressure Regulator and a Return Line to the tank. From what you've said, it seems to me that the genset is being supplied by the Return Line. The Regulator limits pressure to a certain spec for the fuel injectors, and allows any excess (which there should always be) back to the tank via the return line. No problem when the road engine is running, no return flow when it's not.
Trace the lines from Tank to Engine Compartment, or Compartment back to Tank. There should be TWO for Supply and Return, plus a Third for the Generator. Now, trace the Third one.
If God's Your Co-Pilot Move Over, jd
2003 Jayco Escapade 31A on 2002 Ford E450 V10 4R100 218" WB