90 Dodge Shadow fuel pump only runs after disconnect battery

90 dodge shadow, 2.5L non-turbo, approx 90,000 miles, at

original symptom: car died while driving. When key turned to ON you could not hear fuel pump.

original work: replaced the fuel pump and fuel filter

result/new problem: fuel pump only works under "reset" condition.

In depth:
After the battery is diconnected for at least 10 seconds or more then reconnected, then the key is turned to ignition ON (not start), the fuel pump will run for it's normal two seconds. Turn the key off, remove, insert, then back ON, same thing happens. Do it a third time - fuel pump relay does not click and pump does not run. At this point, the relay and pump will not close / run again until the battery is disconnected, pause, then reconnected.

When you repeat this with a voltmeter instead of pump you hear the relay click the first two times again. You measure 12V across the wires of the pump connnector every time though, even the third time when the relay doesn't click and the pump won't run.

This process is repeatable, it happens the same every every time. The old pump was used to test, and the same thing happens. So the old pump was mistakenly replaced. But at least the pump can be ruled out as a problem.

I replaced the Autoshut off relay - same thing.

Looked at the check engine codes on the dash, and only get 12, 55 (battery disconnected, end of test)

Could it be the computer? Don't want to replace the computer if it could be something cheaper. Any ideas where the electrical gremlin is lurking?