Problem solved. Thank you so much for all those who took some time to share some of their expertise with me. Can't convey enough my thanks.
Seems that there are a million threads out there discussing this issue, so just let me close by saying...
Looking back into this thread, my problem was solved very early on, when the EEC was pinpointed after jumping out the EEC test terminal. For what it's worth, I was able to buy a refurbished EEC that was tested with a warranty for a very reasonable price at a national chain store.
Every single thing after that thread was brought about by trying to work through this with less than optimal voltage in my battery. This is a completely stock 92 lx 5.0, that remains garaged and rarely gets driven in the NY winter. My idea of battery maintenance was running the car for about 30 minutes every Sunday during the winter. Obviously, this isn't good enough, even although it's a 1 year old Motorcraft battery. As soon as it was suggested to charge the battery, my problem began to resolve itself. I purchased a maintainer to keep my battery in better shape from now on.
I also began to get frustrated when my problem wasn't immediately resolved when I swapped out the EEC a few days ago. As a result, I kept going back and forth switching out the new and old EECs. This also prolonged my problem. My fate improved when I made a decision to stick with the new one (some of the reason for me switching was that I needed to return the new one within 30 days if it wasn't the cause of my issue). When you remove the harness, it isn't exactly plug and play, and the EEC needs a few minutes to get it's crap together. This is something I should have probably known, but it took me a bit. For example, once everything was corrected, I needed to unplug the harness from the EEC in order to shove the EEC back up into the kick panel. Once I did that and reconnected the harness, the fuel pump would prime again. After shouting obscenities like the father from A Christmas Story, all of a sudden the pump primed and I never looked back. Its almost as if it took a minute or so with the key in run for the EEC to calibrate.
Careful with the EEC test harness, and make sure you get a good connection for your jumper. As with all our plastic parts under the hood of our stangs, years of heat and cold have made them brittle. Be careful when you handle them. Also, as previously suggested, make sure you get a good ground for that jumper. I wound up actually making one with two spade bits (much like on the diagnostic reader) that slid right in to the test port, and stayed put. A crappy jumper probably also cause me issues.
Happy New Year to everyone!