11.5V = Dead Cell?

My Charger was pushing THIS type of voltage when I had a bad battery:
View attachment 1715573501

Check out this chart:

View attachment 1715573503
That chart is ballpark correct for voltage across the battery when its not being charged or discharged, and there is no surface charge.

What your battery charger does is provide power at some voltage above the battery's internal voltage. For a given state of charge, the greater the voltage difference the greater the current flow.
Different chargers work in different ways but a charger that can provide 14.6 Volts to a discharged battery will be providing lots of current.
Providing power to recharge a battery in the 14 Volt range is basically what the car's alternator does.
The ammeter will show how much current the battery is drawing.
When a battery is fully recharged, less than a 0.1 amp will flow when connected to charger or alternator at 14.6 Volts.
In this post is a photo sequence of moderately discharged battery being charged.
Charging Battery with Alternator - Warning

He has added a volt gauge (spliced into the ignition "run" side of the ballast resistor) and with the engine running it reads 11.5 volts.

Will a dead, or dying, battery cell limit the voltage to the 11.5 volts?

The problem is that he's not measuring battery voltage. He's measuring voltage between his splice and whatever ground he's using.
To guestimate the battery state of charge he needs to measure the voltage across the battery when its not in use or being charged.
To do it more exactly should measure the acid in each cell (if it has caps) or put it on a load tester. But to solve his mystery start with the voltage.

He says the car "blows" voltage regulators when he turns the headlights ON.
If the voltage the regulator is seeing is 11.5, then it will most likely continuously "full field" the rotor.
My guess is there are poor connections in this circuits. And/or something may be miswired.
If the voltmeter in the dash was in addition to the ammeter, looking at the ammeter will reveal much more of the story.