Well if the belt is not too loose the alternator is not puting out much. The light on the dash going out indicates some output. You have to have the rebuilt alternator checked out. Rebuilts are questionable.

Certainly it might be something else. But to procceed without checking out the rebuilt may consume a lot of time. The dash light acting as it is indicates the exciter circuit is being activated and by going out when the engine starts some alternator output is indicated.

The alternator output voltage balances against the voltage supplying the lamp in the dash and it goes out. The battery voltage you found does indicate if there is any current output from that alternator it is insignifigant.Or is being used in something else instead of charging the battery. Like the glowplug circuit.. You can have the identical symptoms from a loose belt. Do not be suprised if the alternator is a dud either.

I just re read your post.Disconect your glow plug relay. It may be on all the time. There is no way a charged battery could sag as low as this one is unless a lot was going on during that 15 mile trip. Then read the charge voltage. The glow plug relay remaining constantly on may not be indicated by the glow plug light. Not all that unusual of a fault and fools many.

I am actually suprised the car would even start with the battery voltage that low. It has almost no charge in it or has a shorted cell. Twelve point one volts to me is almost a totally discharged battery. Or the remaining five cells are well charged.

If you own a battery charger hook it up and see if the voltage rises. If not a cell is shorted. Most store clerks will diagnose this as a discharged battery. Another alternative is to sub that battery with a known good one. Make sure to observe battery polarity if you do.