I just started having this same problem with my 1970 Malibu. The other night I took it out for a ride and when I turned it off the GEN light stayed on and my radio kept playing. I wired my own stereo in this car, so I disconnected it from the fuse panel to see if I had some wires crossed up. This didn't fix the problem, so I went to the Alternator and unplugged the little plastic wire harness, not the actual power wire, and the light turned off and stayed off. I know the first reply on here said that if you disconnect that plug from the alternator and the light goes off the alternator is bad, but I am just curious how this works. I have broken an alternator belt before, and that made the GEN light come whiile the car was running, but when it is running right now the light does not illuminate....I guess my question is why would it light up after the car is turned off, and does anyone have any idea why my radio might have stayed on? Like I mentioned before, the radio is wired directly into the fuse box and it is connected to the batt and acc outlets for constant and remote power. I also brought my alternator to a parts store and it tested fine, so I don't know wehere to go from here. Any input is much apprecited. Thanks