For the starter motor, try measuring the voltage at the starter power terminal.
Set your meter to its lowest resistance setting, touch your leads together and verify proper operation. You should get something close to "0", 1 ohm or less depending on meter quality etc. If this doesn't work figure out why or your just wasting your time.
Use the direct current voltage setting on your meter at 20 VDC.
Connect the ground wire or black wire to the frame or negative on the battery.
Touch the red wire to the battery positive it should read battery voltage, if you have a good ground. If you don't try again until you know it's good.
Connect the positive wire or red wire to the power terminal of the starter and press the start button.
You should see battery voltage ~12 VDC when pressing the button. If you do the starter motor has quit, if you don't the next step is checking the starter relay.
Do you have to have the clutch lever pulled in on your scooter for the starter to work? Did you have it pulled in?
https://www.howtogeek.com/318722/how-to-use-a-multimeter/#:~:text=In%20any%20case%2C%20here's%20a,denoted%20with%20a%20V~%20instead.