I have had a lot of people come to me with broken scooters and i'd say at least half were just a vacuum petcock issue. Like 1st thing I check. pull off the covers, get the vac line unplugged from the intake and disconnect the fuel line from the carb (or open the drain screw on bottom) then just suck on the vac line real quick and see if gas comes out.
When it doesn't it's usually a crack or hole in the vacuum line not a petcock issue, and you can feel it. replace the line and bike's back in action.
I saved some old guy once on the side of the road with this issue, nice newer model vespa too. he was an old Italian guy who made sausages and cheese and sold em locally, every time I saw him at the local farmers market after that he'd hook me up with some great snacks. karma? maybe it was beyond worth it to see how happy he was not to need a trailer in the moment, but snacks definitely help haha!