adding a charging fault light

I realize you asked Del, but I have to think the relay won't do it on it's own because the battery would feed it anyway.
Maybe a voltage threshold type device, so ANY time the voltage was below say 13 volts it would trigger the light?
(adjustable voltage threshold would be nice)

The Arduino controllers could do this easily.
My thinking. thank You could use a veristat to control voltage on a test bench. lower it till a 12v relay cut out, read the total resistance on the veristat, and put in a resistor of the same value. When voltage goes below threshold relay drops out. Of course power the test circuit with the Same voltage a Alt puts out under load at Idle.