Well, I was able to remove the entire foot panel and rear plastics all in one piece.
The fuel gauge issue was a non-issue after all. The woman never saw the gauge move and thought there was a problem but it turns out she gets better mileage than she thought. I drained the tank with the key on and the gauge went down to empty right on cue.
I did a valve adjustment, cleaned the carb and installed a new plug and she's purring like a kitten. Nice scooter!