12.5 is definatley to low a voltage. It should be ~13.5v. Do you have a multimeter? If so, leave the car off and disconnect the battery, switch the multimeter to the continuity tester (the one that beeps) and check the line between the alternator and the posotive clip for the battery. It should beep, or give a really low reading as its as close to a short circuit as your likley to get.
Failing that, measure the potential difference between the cars body and the output of the alternator. Also, not sure on a DET engine, but I would imagine it will have a second smaller wire which controlls the regulator, check that is firmly connected, or else it wont charge the battery.
Sounds to me like your alternator is dead to be honest.
Edit- Apparantly I should read the whole post before replying, sounds like youve got it all in hand.
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