-Alternator gave a warning yesterday and then last night (all the lights ON, no doubt).
-Good battery rebounds overnight and starts car just fine with the advantage of a frost heater.
-Alternator still issuing warning.
-Battery taking hit because the DRLs are on.
-If there is no wild screeching, smoking rubber and noticeable vibrations, the ALT is spinning.
-The bad dog-bone has zero relation to the apparent issue.
As suggested, most likely the brushes have worn out. Yeah, some last a very long time! But, we have no history of this ALT or Car. Maybe the IP is leaking diesel fuel down on the ALT. Did the little cover and seal on the Voltage Regulator pull loose due to heat and allow water into the delicate electronics?
Yeah, check the voltage! What will that tell you? Battery is low, due to why? You can put an old weak battery in there and boost-start the engine. If the ALT is working properly, the RED light will not be ON as it charges up that old weak battery.
It's possible to remove the Voltage Regular (which contains the brushes) with the ALT on the vehicle. But, it is a challenge! 13mm, 15mm, 8mm, Phillips screw driver (or 8mm nut, depending), light to see, a mirror, etc. The 8mm wrench/socket is to remove the ground/strap for sure. When removed, if the brushes are the culprit, it should be apparent as others have suggested.
Removing the ALT is a challenge as well. Right Fan needs to be removed. The AC Compressor needs to be unbolted and dropped down out of the way. The Serp Belt needs to be removed and the Serp tensioner needs to be removed.
Keep us posted!