If it is still under warranty drive it to AZ and let them test it. However, you need to have a fully Charged Battery for them to Test the Altanator while it is still on the Car. If they bring out their own Battery to do the test that is OK.

The reason a gave the answer I did concerning the Low Charging Light is that the little bit of current draw that the Low Chargeing Light uses; cause that Alternator to start Charging. Ounce it starts charging something inside of the Alternator itself causes the Low Charging Light to shut off.
Since a Rebuilt Alternator might use components from any where in the World during the rebuild process (Example: some aftermarket Voltage Regulators put out more Voltage than others) I would expect some varation in what Voltage would cause your Low Voltage Light to Light. Maybe even the Wattage of the little Light Bulb might have an effect.

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84 300D, 82 Volvo 244Gl Diesel