OK gang, lemme see if I can clarify this a bit.
The "ignition" light (really a serious misnomer) is connected between the battery and the generator output when the ign switch is turned on. The generator output is zero, so the light comes on.
As the engine starts and the generator output increases, the voltage across the light decreases and when the generator is within about 4-5 volts of the battery voltage, the light goes out. So, in essence, it's a crude indicator of whether the generator is working, more or less. If the generator output is zilch, it will come on when the car is running; if the generator is putting out anything over maybe 8 volts, it will go off.
The light really tells you nothing about whether the generator is charging the battery, or whether the battery is charging or discharging. You can turn on all your lights at idle, and I can guarantee that the battery isn't charging--there is more current coming out of the battery than the generator can provide, so the battery is discharging. Even then, however, the ignition light will be off, because the poor, suffering generator is still putting out the right voltage. Just not enough current to meet the demands of the car's electrical system.
Finally, unless I'm missing something, I have a hard time seeing how the light could stay on after the ignition is switched off--in the bugeye, at least, it is completely disconnected from any source of power when you turn off the switch. Maybe in later cars, the situation is more complicated? I dunno. I have a bugeye.
On the other hand, if the light stays OFF when you turn the ignition switch ON (and you know that the bulb is OK, of course), that could be an indication that the generator is open-circuited, which could be caused by bad brushes. In this case, the light will stay off when the engine is running, too, but the battery will definitely NOT be charging.