Something as seemingly minor as a fuel gauge leaving an otherwise air
worthy plane on the ground... sigh...

Little things can become big things in a hurry.

Forgive me if I'm being really stupid, but I would say flying with a
broken fuel gauge is more than a little thing? :-/

If you run out of petrol in a car, most likely you stall and get stuck
somewhere, if you run out of fuel when flying, the possibilities are
far worse.