That's weird. I converted a Ford 9N tractor to 12v, using a GM alternator, and you had to design a circuit to excite the alternator into charging. After you started the tractor, you had to rev the tractor over 1200 rpm, at which point the alternator would begin charging. This was intentional and how the circuit was engineered to work.
In your case, perhaps you need to find the 'excite' (field?) wire to the alternator and watch its voltage as you rev the engine. Obviously, your case is not normal...
I would think an independent 'automotive electrical shop' (if you have any in your area) could give you some ideas, too. You need the old geezer in the shop that has a mountain of old starters on the floor and an inch of dust everywhere.
Colo Springs, CO
'78 FJ40, '89 FJ62, '98 4Runner