Gemini19th81, I know this post is incredibly old... but to answer your question, Yes, your problem is the Lamp Outage Module. I too have a 1996 Explorer (Limited) and had the exact problem. And in fact, if you do a little research online, you'll notice that HUNDREDS of other explorer owners have been having the same problem too.

The L.O.M. is located directly beneath the message center. You can just pop off the message center screen by squeezing the sides. The cup holder comes off the same way. The Lamp Out Module should be on the passenger side of the console, about where the passengers knee would be. It's got a bunch of wires plugged into one side, it's about the size of a pack of cigarettes, held on by 2 screws. Once you have it removed, you can open it up. there's a few clips keeping it closed, it can be kinda tricky. When you get it open, you should be able to clearly see a burned area around a few of the resistors.

If you want to save yourself $300, you can just use a soldering gun to touch up the burnt contacts, or take it to an electronics shop. I'm sure they wouldn't even charge you for something so simple. Ford should have recalled this years ago. I hope this helps.