Not to run you off but the people at
www.modernvespa.com are better versed in Piaggio ills. Judging by the size of the scooter you're in Great Britain. There are many members there from the United Kingdom.
You could check the Stator with your multitester and see, with the engine running if there is AC voltage coming out. If so there is a bad regulator. Of course check for a bad connection in the charging circuit by tugging on ever connection along its route.
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2008 Eagle Milano 150- 9,679 miles
2009 Honda Rebel 250- 10,434 miles
2009 CF Moto Fashion- 16,023 miles
2009 MC-114 50cc Cub Clone- 4,317 miles
twowheeler.yolasite.com/
That's 30,049 China Scootin miles and Counting.