I *think* it's at about 12.7 (my meter got some moisture in it which causes the LCD display to show 0's, 8's 3's, 5's etc about the same...so it's a bit hard to tell.

What is obvious is with the engine running, the battery still reads 12.7. When I should be getting around 14 at the battery, correct?

 

Yes should be reading at least 14 volts at the battery above an idle. Check the regulator connections to see if a wire isn't making good contact on the terminal board along with making sure the battery connections are tight. Usually a faulty regulator when this happens,but you can check resistance between the yellow wires leading from the stator.Should be some resistance between each yellow with no yellow shorting to ground. If that checks out,replace the regulator.

 

Where is the stator? I see a connector going into the top of the "pull start assembly". Is that it? Even at a high idle, still only 12.5V

 

Yes.. you will have a solid yellow in most cases and either a yellow/red,yellow/brown or all three. Trace them up from the stator harness. Test resistance between each one,yellow to yellow/brown,yellow/brown to yellow red,etc. Should be a small amount of resistance between each wire to another and no yellow should short to ground. Just have the positive lead in the wire,negative lead to frame or brown ground wire. Shouldn't zero out to ground on any wire indicating a short. If this checks out,the most common problem was a faulty regulator or problem at the connections.

 

Looks like it has to be the regulator. Everything else checks out good.
Hope I can find one not too expensive!