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Thanks for posting
As you said and which is correct, the ECM supplies the ground path to turn the C/Opn relay on. The ECM needs a couple of signal verifications like rpm(cam and crank angle), spark confirmation etc. When the ground is lost something is missing that the ECM needs to see. Have you checked for any diagnostic code information?
Is there an Autozone or O Reilly close by? they read codes for free, you could also invest in an inexpensive basic code reader.
I will have to get back to you tomorrow morning.
The wire that is supposed to be grounded by the ECM is intermittently not grounding and that's why the pump won't run we have established this so far, what I'd try is to run a jumper from that wire on the Copen relay directly to ground, the pump should then run and the engine start, keep in mind this is only a test. Let me know how that goes.