I have to agree with CO on this one. The thing I find troubling is that your lights dimmed but no fuse was blown. [emoji848] Typically that would suggest a weak battery (which doesn’t sound likely here) or A LOT of current being drawn somewhere.

Dunno.
 

Only 2 wires attach directly to the +  battery terminal.  One is this one, and the other goes to the starter.  

8 hours ago, iufan993 said:

The battery terminals were fine, but this spade connector on the positive side near the firewall was corroded.  Problem solved.  

Should say "Problem disappeared.".  They do that sometimes.

Your solution didn't match the symptoms.  That's where the extra commentary is coming from.  You might be back.  Good luck.

5 hours ago, iufan993 said:

Only 2 wires attach directly to the +  battery terminal.  One is this one, and the other goes to the starter.  

Right. One of them (the big one) goes to the starter, and the other one powers the EFI system (and only the EFI system).

The rest of the car (everything except the EFI) is powered off the white wire is connected to the other end of that big (+) battery wire down on the starter.*

Next time it happens, wiggle stuff around and see if you can pinpoint where the issue is. Battery terminals up on the battery. Other end of the (+) wire down at the starter. Wiggle the fusible links. Wiggle the body ground wire next to the battery below the wiper connector.

Happy hunting, and here's hoping you find it.   

* Want proof? Disconnect that EFI spade connector and then turn the headlights on. They should light up. Then try to start the car. The starter will turn the engine over, but it won't start.

OK I get it.  I just brushed and cleaned all of the starter terminals and wires to keep gremlins away. 

Cool. Hope that keeps the gremlins away. And if it does come back, think of it as an opportunity to find and put a stake it for good. Haha!

So remote electrical troubleshooting over the internets is always questionable. But from here, it really sounds like a poor connection in the main power branch of the car... Battery terminals and cables, starter wiring, fusible links, shunt assembly, some big ground connection near the battery... Something like that. Not the ignition switch.

Hoping you already took care of it and you're good to go!