Checking for charge output. There are more accurate ways but what you've already done is exactly the method I used. At idle you may not see any rise in battery output but at full throttle it should work its way up to around 13.5 volts/

Your system probably has a simple diode in line between charge coil and battery acting as rectifier to convert AC to DC. Unplug the charge wire at first point past diode on the way to battery. The diode is in line and sealed in heat shrink tube. Stick a straight pin into the wire on both sides of the diode and ohm test for continuity through the diode. If not familiar with diode testing you should show continuity in one direction but not the other using your ohm meter setting and reversing meter leads. If you get continuity both ways or neither way the diode is bad and replacing just the diode is probably all that is needed. You can cut the diode out, strip off the heat shrink and go to Radio Shack to get a matching diode and then splice it back in.

If diode is not bad or you're not up to the cut and splice you'll need to replace the charge coil which comes with the wired in lead and diode.

Bob