First thing I would do is to remove the spark plug when the scooter doesn't start, then ground the plug against the tappet cover and swing the starter to see if you can see any spark at the spark plug.
If there is no spark, you can do the same test on a new spark plug.
If you don't see a spark at the new spark plug, you should do an Ohm test on the ignition coil to see if the the coil or plug wire is not faulty.
If the ignition coil is not faulty, the CDI or ignition switch might be faulty.
In short, you can save a lot of time just by checking if there is any spark at the spark plug.
If you see sparks at the plug during the test, it means the problem is fuel related, and not an electrical problem.