Trying to figure out what a plug is in fuse box?

The image didn't make it through. Perhaps you can find it listed here and report back?

Okay, that is the Electrical Load Detector. It is a feedback circuit that tells the alternator how much and when to charge the battery. Inside the box it is a loop that goes around the primary electrical feed buss connection for the van. What is it that you are doing to it? Unplugging it or just pushing it around a bit? Either way it sounds like the main conductor in the box is loose and your moving of the ELD is making it connect. Because of the design that part isn't an individually replaceable component, you replace the entire fuse and relay box. So, you make sure you have any theft codes for the radio and nav system, then disconnect the battery, then unbolt the box and remove the electrical connectors. Reverse the process with the replacement and then perform the idle relearn and if needed enter the codes back into the systems to unlock them.

Okay, it sounds like there is a bad connection inside the relay box. Moving the connector is shifting something in the box. If you unplug the ELD it should only shut off the alternator, it shouldn't cause a no start. Your description of the way it starts sounds more like a fuel pump power issue. The way they normally work is that you turn the key, the pump turns on for a couple seconds. Then it shuts off. While the engine cranks it turns the oil pump, when the engine fires and the PCM now sees an rpm increase and oil pressure it turns the pump relay back on and the engine runs. A loose connection or corroded fuse that moves when wiggled would act the same way. It might be worth the time to disconnect the battery negative and then pull and inspect the fuses and relays in that box. Including the large bolted fuses 41 and 42.

Okay, let us know what you find. Hope it's just a corroded fuse.