Brian, I got your email, I don't know that i really have more to contribute than what the other's have been saying.
In post #12, he said it was the EEC fuse that was blowing. For now, I will assume that is still correct.
EEC fuse can be a tricky one to track down. Interestingly, just the other day, I was browing through the Haynes manual for my Suburban, and found a brief description in the Chassis Electrical section describing use of a self-powered test light (aka continuity tester). Never used one, but I thought that it seems like the perfect tool for tracking down a short like this. Basically, if the current from the test light can find a way to ground, the light comes on, if it can't the light stays off. Unplug everything the EEC-IV relay feeds power to (Shamaal's wiring diagram seems adequate, but I didn't look real close at it). Plug a continuity tester into the red wire at the EEC relay connector and see if the light comes on. If the light comes on, then the short is somewhere in the harness still connected to the relay connector. If the light stays off, then start plugging connectors in until the light comes on.
It seems like BrooklynBay has mentioned use of a continuity tester in other applications, he may have a better grasp of how to use one to find a short like this.
Good luck.