Had the charging light come on dimly at the end of about a 20 mile drive. Changed the alternator, but after a similar length drive, it came on again. Found what I'm pretty sure was the issue: a poor contact at the junction at the solenoid where the alternator output goes back to the battery. The old alternator was probably fine (glad I kept it).
But I have a theory about why it only seemed to come on after driving about that far that I wanted to check. The light has the battery + on one side of it and the alternator output on the other. Since the alternator is supposed to feed back to the battery, those voltages should be the same when the car is running. But if you have a bad connection back to the battery, then the light is only getting 12V from the battery side, but maybe 14V from the alternator output side, a difference of 2V, so current flows and the light comes on.
When the battery is nearly charged, like when you've just driven a bit, the alternator outputs less. If you have a smaller voltage difference between the alternator output and the battery + it will not be able to overcome the additional resistance of a bad connection, because you need volts to break down insulation. That's why the light came on at the end of driving a few miles like that, but everything seemed fine when you started the car from cold, because it had a bigger voltage to charge the recently exercised battery.
Does this sound plausible?