Well guys, after all of the great responses from all of you, I guess I'll have CROW for breakfast. I finally got my old eyes and flashlight working together and found that the battery is indeed installed backward. It was that way when I bought the car. As for the ammeter registering correctly, it must have been my imagination. I'm going to take the battery out and completely discharge it, and see if it will charge up correctly. If it doesn't, I'll buy a new one.
Many thanks to all of you for the head scratching and comments. Looks like the first person to reply was right on target.