Is it just the fuel gauge? or is it something to do with the tank/float? If it's just the fuel gauge, there's probably lots of people here that will sell you one. If it's the tank/float, then that's a different matter, but there are probably fixes for that posted here, or someone here can tell you how to fix it.
He has two other cars for sale online. On Evil bay, or C-list? Is he a regular car seller?
So let's say in all fairness, he's being truthful, and he just doesn't have the time - he's that busy.
Then, as far as I can see, he's gonna be too busy to help you with questions, too busy to get you the pics you need - Basically, you still don't know much about the actual condition of this car.
Still, if a person is that busy, and would take the time to do a video, wouldn't you want to at least do a decent one, so you don't have to do a second one, or a third? (I still question this.)
If that was me, I'd do a good video once. have a nice slow pan of the outside showing any damage, and then showing the inside. then under the car. Then I'd show it starting up and running and/or driving.
It's really hard to make a decision to buy a car, when you can't see it very well.