Why does the gen light stay illuminated in my 1972 Oldsmobile cutlass supreme?

Your alternator is NOT putting out enough voltage to keep up with the amount being used. This can be casued by: The belt slipping on the alternator pulley The alternator is going bad. I woudl see if the belt is tight and is NOT slipping. If you haven't bought a new belt lately, its a cheap investment. If the belt is tight and the alternator light stays on, take the car to Autozone or Pep Boys and have it checked while on the car. If you have a multimeter you can check it by seeing how many volts are comign out of the alternator by placing the leads on the alternator to see what current is being generated by it. Anythign less than 12 I would buy a new alternator. Most cars need over 12 volts to 14 volts to operate. Most of my cars run 13-13.9 volts. Also, check the voltage regulator which is located on the fire wall below the left windshield wiper. This a cheap part which often fails on that model.