It sounds like the scooter has low mileage, but it's not under guarantee any longer ? If there is no guarantee in place at the moment, I think there is a possibility that a proper load test needs to be done on the battery.
I wouldn't be too worried about the brake lever switches. Those switches works independently and chances that both switches are faulty at the same time are almost zero. "Works independently" means there is no need to pull both brake levers at the same time to start the scooter - you just need to pull ONE brake lever, and the scooter should start.
The brake switches only complete a positive (+) power feed to a single wire - and the far end of that single wire is the actual thin wire which get connected to the starter solenoid.
So you can easily check both switches individually, just by removing the thin wire at the starter solenoid - and doing a Voltage test at the terminal of the loose thin wire when you hit the starter button. You obviously need to pull each brake lever individually when you hit the starter button.
If any switch in your case is faulty, I think it would rather be the starter switch itself - as mentioned, chances that both brake switches are faulty at the same time are very slim. If you do the brake lever Voltage test (as describe above) and you get a proper voltage reading, it obviously means you don't have to worry about the starter button (switch) either - it will also be in perfect condition.
In short - I guess the problem is rather caused by the battery, loose or bad battery connection, or the starter solenoid itself.
