The most likely cause is a wire losing it's connection someplace more probable due to either corrosion to a wiring pin or connector harness or a wire pin is backing out of a harness connector should you not be able to find a chaffed wire to either the fuel pump circuits power or ground sides or Key On Ignition side circuits.
You may want to try continuing with inspecting and multimeter testing each wire circuit individually that has some sort of partnership to the fuel pump and key on 12v power and ground circuitry including the relay wires and ECM wirings for each circuit... For guidance, the wiring circuits can be found online inside Mercruiser service manual number 36.
The following link is just meant to be one example of many to use to help get an idea of what you might be looking for as to possibly having a corrosion issue someplace within a wiring circuit or wiring harness connector either at the cannon plug, a sensor connector, fuse holder or relay harness connector, etc.,
http://www.marineengine.com/boat-fo...Mercruiser-350-Mag-Starter-Continually-Cranks
While it could be an internal ECM issue, you may be better off trying to first eliminate the wiring system as that is typically the first to fail under normal circumstances meaning nothing known has compromised the ECM such as water ingestion, battery cables connected backwards, lightning strikes to the boat, etc. etc.
If you still suspect a bad ECM then there is a repair facility in Fresno, CA that you could send in your design model 555 ECM for testing and possibly have it repaired depending on damage before having to decide on buying a new ECM.
https://whipplesuperchargers.com/index.php?dispatch=products.view&product_id=73
Though it seems the repair cost went up $100.00 to now $600.00 the last price I've heard for testing the ECM to ensure it's "good"/diagnose was $100.00 but not sure now. It's best to call them first.
Since you were able to wiggle things around and it seemed to work at some points, stay on the wiring connections before buying an new ECM as something would appear from your description of being overlooked.
Let us know, good luck.