This is actually quite common. Suggestions are to clean all the connections in the fuse box (remove the fuses and clean the contacts). The blade type fuses should be pretty reliable but the older 'bullet' style fuses can look OK but not work right. If you have the bullet style, I'd say just replace them since they could be 20 years old.
Next, there is a junction box on the left, inner fender (in the engine bay) with 3 or 4 red wires and a pair of green wires. With the battery cables disconnected (to avoid a short), remove the cover of the junction box (although sometimes it is already missing...) and clean the terminals there.
Some have found that replacing the red wire between that junction box and the alternator with a new, larger guage wire fixed the glowing battery light. Also, I assume the alternator is grounded via it's case. Thus the connection between the alternator case and the engine block must be clean & tight.
If all of that doesn't fix it, you may need to investigate the connectors behind the fuse box. I found some were loose. And next, it could be the ignition switch itself or any connectors between the ignition switch and the fuse box. Likely it is combination of more than one iffy connections. Clean and tighten any you can find!