Battery Light Comes On Intermittently.

What is your question?

When I start the car the battery light stays off for a couple of minutes then comes on. It'll stay on for a few minutes then goes back off and on intermittently. I just replaced a 10 year old battery at Advanced Auto and they checked the charging and starting system and it's O.K. What it seems like to me is that the light is off while the battery is charging and comes on when the battery is up and then goes back off when the battery is down a little and needs some more charging. Does this make sense?