Originally Posted by tomw

The word I was looking for is 'calibration'. As the model year progresses, the manufacturers may come up with some new whizbang combination of emission settings that will save the world and make sliced bread look old fashioned. This combo is called a calibration, thought that is not what the word originally means. If your engine was set for a specific calibration, then a one-size-fits-all ECM may not work correctly.
If you could re-install the old one, you might find that there is nothing wrong with it. Ford has a very good record for their ECMs, with few failures.
Any of the relays- fuel pump, ECM, headlight, trailer light, fan or whatever do not run hot when energized. They may be warm, such that you can hold them in your hand with no problem at all, but not hot.
I would watch the pin on the ECM that grounds the fuel pump relay. It should ground for about 3 seconds, then shut off. Your relay apparently is being grounded for a second, and it may be that it is drawing too much current. Check it as noted to see the draw of the relay itself, not what it is powering, though it would be a good thing to know how much the fuel pump(s) draw. They draw more amps as they age, apparently, and your pump may just be on the fringe of acceptable draw. That would not explain the relay functioning the way it does, though. If it had been me, I would have replaced the relay before the ECM... a lot less dough.
tom