a little understanding of how that light works will help you understand the issues involved, so here's the basics
the ignition circuit supplies +12v from the switch to the alternator, via the bulb, when the alternator is not turning that wire will be connected to earth (-) inside the alternator therefore the circuit is completed and the light comes on, now, when the alternator is spinning (and this is working on the principal that modern alternators are all 'self-exciting" and don't require a separate +12v supply before producing an output) the alternator will supply +12v to the connector the bulb wire is connected to, thus breaking the earth (-) line and breaking the circuit, so the bulb goes out, now if the alternator is not spinning quickly enough, the alternator will still give a connection to earth but with more resistance on the line, thus making the bulb dimmer(just like wiring 2 bulbs in series), this will also be the case if the brushes wear and become intermittent in their contact inside the alternator, and also if the regulator pack starts to die it will "leak" the connection to earth thus making the light come on dim or intermittently, these effects can be seen much better with a volt meter and amp meter fitted to the circuit.
it should have nothing to do with over charging, unless the regulator pack dies on that side of the circuit as well, and then simply keeps charging the battery when it doesn't need it, this can happen on its own without the light coming on, or the light can come on without the battery over charging, no way to tell this without having the alternator thoroughly checked, and this is not worth it money wise
short answer .... buy a new alternator, or change the regulator (diode) pack and brushes
and im happy, 