Don't know where the fuel pressure to the gen is coming from, that shouldn't be happening, but fuel coming out of the carb at the air intake indicates the needle in the bowl of the carb is stuck open.
Open the fuel cap to vent off any pressure in the tank. Only two things will run the fuel pump on the gen, the gen is running or the fuel prime is on. Neither has anything to do with the chassis engine running.
Stuck needle valve is probably caused by gas sitting in the gen carb for a long time, evaporating, and gumming things up.. It is difficult to actually see the needle with the bowl on the carb removed. With the bowl removed the needle should move up and down with the float. A little carb cleaner sprayed at the needle bottom should free it up.
Don't try to take the float out unless you remove the carb.
Yours is very similar to my Q-55G
2000 Sea Breeze F53 V10 - CR-V Toad
Some RV batteries live a long and useful life, some are murdered.
Get a Digital Multimeter and Learn How to Use It