Woohoo! I got rid of the alternator light just now! As it turned out, this red wire was disconnected from its point and (I assume) was touching some part on the alternator. The red wire is quite thin and seems to be coming from the black box that sits next to the coolant resevoir. The connector part mates to this flat metal piece on the rear of the alternator. I guess it must have came loose and thus causing the alternator light to go on when the key is released. I reconnected the wire and, voila, the light goes off! In addition, after reconnecting the wire, I realized that my other idiot lights (e.g., Lambda, Brake, and Bulb failure lights) were operating normally--didn't realize they weren't when the red wire was disconnected.

Now, I have some questions. Could my alternator or any part of my electrical system be damaged (even slightly) by the metal tip of the red wire touching the metal part of the alternator? And the fact that my car was left over night with the Alternator Light lit up on the dash, will that do any harm? Did anything get fried?

To leave on a positive note, my car started right up this morning, which really surprised me. And after plugging back the red wire to the alternator, I checked most of the electrical components--all lights work, radio works, and fan works. But I would still like to know if this Alternator Light and the disconnected wire caused any unseen problems. Thank you all for your advice!