Hello,
I've searched the forum and found many similar problems posted. But not quite like this.

92 Explorer, 4.0L 5-sp manual

I put the key in and turn to the "run" position. The instrument panel gets powered and everything looks ok.

I depress the clutch and turn the key past "run", to the "start" position. I hear a click (presumably the starter relay), then the instrument panel goes dead. In fact, everything goes dead and stays dead. Total power blackout.

At this point, if I try turning the key from "run" to "start" again the gauges may flinch, or do nothing at all. The power eventually magically restores itself. Sometimes after only a second or two, sometimes after a couple of days.

I've tried jiggling/tapping to discover the trigger that restores power, but to no avail. The battery seems ok, every connection I could get to seems ok.

Having read the other posts I am now confused as to what is meant when they say "jump the solenoid to see if it is bad." Do they mean the relay (up on the fender wall next to the battery), or the solenoid down on the starter motor? Actually, it's not clear why either one of those being bad would cause the total power blackout. Just thought as long as I have your attention I could get that straight.

Any suggestions would be greatly appreciated.

 

I would start by removing and cleaning the battery wires, positive and negative both ends. Also make sure the battery is fully charged.
Sounds like you may have a dirty/corroded connection, and as soon as the starter tries to draw a lot of current to turn the starter the connection "opens".
The solenoid/ starter relay is the one that the battery positive wire feeds. Most of the trucks I work are not manufactured with a year staring with the number 9 but Iwill guess and say the starter relay is similar.
Anyway there is 2 large terminals on the relay. One has the battery + wire on it the other has a wire that runs direct to the starter + .
So one way to jump the relay is to connect the 2 large terminals together, with a jumper cable or other large wire. This send 12 volts direct to the starter bypassing the relay.
Another way is to use a smaller wire and jump 12 volts to the small terminal on the relay, could be 2 small ones or 1 depends on the year of truck, anyway if 2 small terminals jump to the "S" if 1 small terminal jump to it.
This way closes the relay, but bypasses all the neutral safety switches and the igntion switch. So make sure the truck is in neutral or park if auto, I know yours is a manual but just in case someone with an auto reads this
Good luck. May just be a bad connection at the battery.

 

your battery terminals are corroded. get a cleaner and you'll be fine. same thing happened on my truck recently.

 

The most common reason is a corroded battery connection like everybody else said. Another uncommon but possible reason is a intermittent dead cell in the battery. Also don't forget the connection where the ground wire connects to the engine block.