Strange charge light issue

Hello all, my jeep is being a pain again. Here goes. 1985 jeep cherokee xj. 4 cyl. Auto 4wd. When the key is turned off the charge or battery light comes on. I end up with a dead battery. When the key is in the on position the light goes out and dosnt come back on until I turn it off. Once I jump it off it runs fine, no charge light. In fact, this led me to believe that the alternator is good, because once it is running the light5 goes off and the jeep runs fine for as long as I want it too, even when I use the headlights. The battery has been replaced. I realize I can have the alternator checked easily, I just have not had the time yet. When I was checking alternator prices on the advanced site, listed with the alternators was a statement that said that a blown fuse or bulb in the warning system could result in a no charge condition. HUH? Obviously the bulb is good since I am sick of looking at it, and if the fuse was bad then surely the bulb wouldnt light at all, right? Help please. Thanks for any suggestions.