Ian, I will assume your generator brushes are good. If you're not sure, give them a check. New generator brushes are cheap.
It's important you understand how the GEN light works.
On one end, the bulb is fed from your key switch (positive).
On the other end, it's fed from your generator (also positive).
So, now we can measure the difference between your battery voltage and your generator's output voltage.
When you first turn the key on before starting the engine, your GEN light shines because the generator is putting out nothing but the battery has 12-volts.
If you throw a belt, your GEN light shines, for the same reason.
If you have your accessories on and stopped at a light, your GEN light might flicker because the gen is putting out very little at idle speed but the battery is at 12-volts.
Ok, I led you around the barn. Now the real answer. You may have a voltage regulator that is bad. The voltage regulator supplies field voltage to the generator so the gen can produce power. Without field, the gen puts out nothing. Without a belt, the gen puts out nothing. Even still, that important GEN light draws a comparison to tell you if your system is charging or not.
ALWAYS make sure your GEN light works. If you turn the key and it doesn't shine, buy a new bulb (I think it's a #57).
How do you know when the battery is charging? Put a voltmeter across the battery terminals and look for 13.5-volts or more when the engine is above idle speed.
To prove your generator can produce, jumper the BATT and FLD terminals on your voltage regulator and watch the voltmeter on your battery climb. Don't leave the jumper on for long because you are bypassing all voltage regulation. I use one minute intervals.
When the generator is charging, you can hear the engine speed go down and sometimes you can hear the generator as it produces power. Hope this helps. - Dave