I'm like chawk_man in that I don't know the 130. But in my experience with efi, I don't think the injectors should fire or the pump should run constantly.koeo (key on, engine off)
If it's doing this while cranking, then THAT may be normal. You didn't explain the scenario fully enough for us to know.
Since you say one outboard is fine, the other is not, says you have an issue and I'm only guessing it's doing this koeo. And, in that case, I agree with swapping ecu's
BUT...smell them before plugging them in! They should both smell the same! If the suspect one smells acrid or smokey, you shouldn't plug the "good one" in to the suspect's harness until you've eliminated the possibility that the harness or a sensor could have failed (shorted out) the ecu.
Good luck.