What does it mean when the battery light stays on in a 1995 Lincoln Mark 8 for two weeks after the alternator has been replaced?

re check the two wire connector to alternatorDid you check the Battery connections? Typically, you want to replace the battery with a new one when you replace the alternator.

Are you getting any messages in your message center? Stuff like "check Charging System"?

What voltage is the battery sitting at with the motor running and the lights on?

did you consider the alternator might be bad? Yes, I know, new alternator, but that doesn't mean it's always 100% good.