You've got a 'parasite' that's draining the battery and this needs to be checked out by a vehicle electrical specialist. If you are using a very high rated AH battery, (100AH rather then 60AH) for which your vehicle was not rated for, this will cause the alternator to 'overcharge' the battery as the high rated battery will take all and more power from the ...
The 12v pin on the OBDII should be constant on regardless of the key position. Here is the pin out:
You can test it with a multimeter to ensure it is this way in your vehicle.
Whether it will work for trickle charging with a solar panel has yet to be seen, but always worth a go.
Where did you test the AC voltage? In the leads coming out of the stator? Or the leads coming into the regulator?
It's possible there's a short/bad wire on the AC wires between the stator and the regulator.
Where did you test the DC voltage? In the leads directly coming out of the regulator? Perhaps there is a short somewhere there.
Was the regulator ...