I had the same 4wd high/low lights flashing on/off and 4wd would not engage on my 1998 EB Explorer. Friend told me to disconnect negative cable on battery for few minutes, then reconnect and try. I did not think much of that idea, but Googled it and found a couple references to doing that with success. I then clicked on Serious Explorations for more input as to solving problem.
I figured what the heck, try the easiest thing first, so did the battery disconnection thingy. Disconnected for ten minutes, reconnected, started engine, put in neutral, moved switch to 4wd low, nothing for a couple seconds, then shazam, clunk, and engagement with 4wd low light on. Ran back and forth on gravel drive, switched to 4wd high, engagement with 4wd high light on, ran back and forth again, then switched to auto, 4wd high light cleared. I repeated process few times with same results. Don’t know if battery disconnect cleared computer faults, or if problem will repeat later, but for now all is A-OK. So owe my bud a six pack.
By no means am I implying this will work in all cases, but like lunaka in post above, just know it did work in this one instance.