Generator for Travel Trailer (not a tech question)

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I'd run the cord. It's a lot easier to lift than a generator.
I once wired a friend's camper with an auto transfer switch. I installed a generator inlet and cord on the tongue and ran the wire for that back to the generator terminals on the ATS. This allowed him to just use a short cord from the trailer to the gen. in the truck bed. I think he left it hooked up all the time. Anytime they stopped and wanted power he just had to start it up.

Looks like a TT manufacturer would provide a place for a generator.

I would mount it on the rear of the trailer. But make a platform that sits over the frame and bumper and then reinforce that area. THen you could mount it solidly however you want. Don't put it on a cargo carrier that slides into a bolt on receiver because that will be too far back and will allow it to bounce and weaken the bumper and possibly lose the generator.