Battery voltage drop

It does not matter which field tab is grounded and which is fed by the VR; all it needs to do is set up the rotating magnetic field one way or the other inside the alternator. At least you now have it charging.

Did you run this for long? One thing going on is that your battery is not at all charged. In fact with it down at 12.0v it is at least half discharged. Under those circumstances, the outputs will be low, especially with a 35A alternator, because the alternator is doing all it can just to charge the battery.

The 10.25v on the field indicates that the regulator is commanding as much field current to the field winding in the alternator that it can. It may be due to the battery discharge or may be that the regulator is not seeing full voltage; I would suspect that this is due to a discharged battery at this point. When things are normal and well charged, the filed voltage will be a lot lower.

I would do this so we can get good measurements to see if something else is going on: Charge the battery overnight. Make sure that the battery is near to full charge; you can tell this if it reads 12.6 or 12.7 v after you have pulled the charger off for a 30 minutes or an hour. Once charged, put the battery back in, and then retest the battery charging voltage test to see if it is good.
- Check the battery charging voltage for the 13.7 to 14.3 volts at fast idle, alternaotr warmed up.
- Measure the VR voltage into the ungrounded field terminal like you did and let us know.
- Check the power feed into the VR (the blue wire) and report that too. If you have voltage drops in the harness, bulkhead connector, and/or ignition switch, then the VR will see too low a votlage and react by commanding the alternator to too high an output voltage to try to compensate. But that is not happenning (yet).

But, right now, with a partly discharged battery, the voltages will be off. BTW, if you choose the drive the car instead of using the charger to re-charge the battery, then you need to drive for a half hour or more to get a good charge into the battery.

I would also let the battery set disconnected for several hours after charging to see if the 12.6 or 12.7 volts holds for several hours. If that voltage drops disconnected, then the battery has a problem. Or, take it to the auto store for testing. A partly shorted battery cell will also hold down the charging voltage.