This is as simple as I can make it: There's a transistor inside the ECM which is connected to pin 4 on one side and ground on the other. The transistor isn't shown on the wiring diagram, but when the ECM activates the base (trigger) of the transistor, the transistor acts like a switch turning on and conducts whatever is connected to pin 4 to ground. In this case, that's the coil of the ECCS Relay. Since the other side of the relay coil has 12V from the battery, whenever pin 4 supplies it ground, the relay coil conducts and the relay switches on. The reason it's arranged that way is so the ECM can "wake itself up" to do vacuum testing on the fuel tank when the car is parked, even though the ignition is off. But it's also supposed to wake itself up immediately whenever it sees the key turn on. That's what it wasn't doing before you jumpstarted it.
I did a writeup for Nico about how to chase short circuits which you may find useful. In this case you might end up doing segmented fusing like in Part 3 to get to the bottom of it, since it's obviously intermittent and the short could be a dying component and not just wiring.
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