You need a voltmeter to test the charging system. Most buy a digital multimeter (Wal Mart or Sears about $20)
Then charge the battery fully. Put the scooter on the center stand and open the battery box if not already open
Measure the voltage at the battery with the engine off. (12.5 volts)
Start the engine and measure the voltage at Idle (may be below 12.5)
measure the voltage as you increase the rpms: at 2000 and 3000 rpms
The voltage should increase as the rpms are increased and reach 13.5 to 14.5 volts, but never excess 14.5 volts.
There is no need to exceed the 3000 rpms in this test.
AND you need to be sure that the rear wheel does not touch ground as you are running the engine and making the voltage measurements.
If the voltage on the battery never increases beyond 13.5 volts then there is a problem with the alternator or the rectifiers.
If the voltage exceeds 14.5 then there is a problem with the voltage regulator.
If the voltages are good, then the battery needs to be tested under load at an electric shop or auto parts store.
Ride Safely,