Sounds like it may be a faulty ignition switch.
First, check the battery with a multimeter to see if it the charge is all the way up. It it is, since you've had an intermittent problem, it's most likely the ignition switch. You can take it out and see if a wire is loose or frayed. Other than that, you'd have to install a new one.
It's easy to get behind the glovebox and check for a loose or frayed wire.
See here:
https://modernvespa.com/forum/topic7819
P.S.: Have you tried to start it holding each of the brake levers separately? It could possibly be a bad switch that engages and allows the scooter to start when you pull the brake lever.
⚠️ Last edited by XLR8 on UTC; edited 1 time