Battery voltage drop

OK, well the battery is not in bad shape; with a 12.5 volt reading after a partial charge and sitting all night, it is decent. And the fact that you get a 14.3 battery charging voltage after the battery charge says that that the alternator is putting out decently.

Now the final thing to check out is why the VR output to the field is at 10.5V, which is high for fast idle operation. But that may be fine at low idle, because the alternator cannot put out much at low idle and the VR will push more juice into the field trying to compensate for that. Measure it again after driving to and from work today at both fast idle and low idle. Also measure the voltage to the VR's blue wire at both low and fast idle.

While you are at it, check the screws that hold that VR to the firewall and make sure they are clean and making a good ground. The VR case needs to be well grounded to chassis for it all to work right. (Some of these older VR's have a separate ground lug on the case that can be grounded but yours does not look to have that.) The same goes for your battery to engine ground and for the engine to firewall ground.