Not running at 12.8, that was sitting off voltage.I'm confused. If it shows 12.8 with the scooter running, its a charging system issue. It can't show 12.8 and 14.ish at the same time.
Charge the battery with one of the cables disconnected. Not with a little ,2 amp charger, but a real battery charger. It should read 14.6v after more than 20 minutes at 10-15 amps. That fist little voltage bump is a surface charge. Then after it sits for 12 hours off the charger and disconnected from the scooter, it should still be 12.6 or a little more. Now load test it at its rated amps. That little hand held thing you see people use will not test it at the rated amps. They top out at 50 or 100 amps. If it passes that, the battery is good. Charge it back up and reconnect the cable.
The charging system is easy. No grounds on any of the stator leads. ZERO. Then spec voltage between any two of the stator leads at the prescribed rpm as per the factory specs. That's Harley specs, not something some third party says it should be. Inspect both sides of the plug while its split. The regulator needs a good ground, so that means the fram needs a good ground. Don't trust an ohm meter, voltage drop it. Then inspect the positive circuit from the regulator to the battery. No repairs, or splices should be trusted. And the eyelet at the battery should be soldered. The regulator runs its own show. If there is AC currant from the stator, it rectifies it to 12 volts with diodes, then feeds enough DC current to the battery to maintain 14.5 or there bouts. Any extra current is shunted to ground. So usually, any funky work one day not the next stuff is rooted in the regulator. Any current flow with the motor off, on the lead to the battery, is a bad regulator.
One other thing I see on those old scooter a lot is they are missing the shunt between the battery and the relay where the wire from the regulator is attached, Not sure about that particular scooter, but on a 94 Ultra the wire from the regulator attaches to the main relay on the negative post. There is also a red wire on that post. The positive post (copper) has a black wire that attaches to the positive battery cable at the starter. And there is a lot that can go wrong there. So for diagnostics, just connect that regulator wire to the positive battery post.
I'll read through your reply tomorrow and check through the system again.