Wow....why do you guys do it the hard way?
Take your voltmeter and put it across the battery terminals when the bike is running. If it reads 12v or less then the battery is not being charged. Not sure what the operating voltage on a bike is but I'm assuming it should be 13.8-14v, like on a car.
From my experience, a voltage regulator usually ( I said usually) allows the battery to over charge when it's faulty.
So, I'm going to take an educated guess here and say your stator is the culprit.....
This sounds very similar to what I did. It'll tell ya in the service manual what it should be charging at.
And at 12K is around the mileage that a lot of people were starting to have trouble with their stators. Mine went out around 22K-25K if I remember correctly. My situation was horrible, was stranded in the middle of no where at night, in the rain about an hour away from home.