Battery indicator light is operated by the voltage regulator. If regulator voltage drops below a certain level, the light illuminates. Does not necessarily mean the alternator output is zero, though. It may still be enough to sustain the load needed to run the engine only; night driving might slowly discharge the battery. Best check easy to do: measure battery voltage at the terminals with engine idling. If 13+ or better, alternator is working: battery voltage alone can never be that high. Turn on headlights and heater/AC blower on high, check voltage then. If it drops much, alternator is asleep.
Shut off engine, leave voltmeter connected. Have someone start engine. While it cranks, just before starting, note voltage. If less than 8 volts, check condition of all battery cells with a hydrometer; costs about 5 bucks. Hydrometer shows state of charge by density of the battery juice. Also shows up a bad cell, which stops battery efficiency greatly. imp
