When I turn the key to "ON", the fuel pump does not kick in.
If I remove the relay, and jumper the pins, the fuel pump works.
When the car is running, and I turn it off, the fuel pump runs a few seconds then turns off (from the oil pressure bypass).
Relay tests good, and I have tried a second relay (new).
Ground and power to the relay test good.

There was an issue with interment power that was related to the connector below the ECM. The connector was replaced and at least this one issue was resolved.

When I remove the relay and measure the voltage from the ECM (dark green / white), turn the key on, I get 12v for a few seconds, then it drops... this is expected.
Connect the relay and do the same test, all I get is about 0.7 volts?

Thoughts on what may be wrong or next troubleshooting steps?
Can I verify the ECM is working correctly?

Take the console off and preform the same test at the Dk. Green/Whitew wire at the ECM. Do this with the relay disconnected first to make sure you are on the right wire. Again look for the +12v when it kicks on an then for it to drop 2 sec later. Depending on if you have a 4 cyl or V6 the wire will be in a different place but I think there is only one or two Dk/Green/White wires on the ECM so it shouldn't be hard to figure out which one has the +12v for two seconds.

Anyways once you figure out which one, then plug the relay back in and try it again. At the ECMs connector does the voltage level also drop to almost zero? If so then you are looking at a bad ECM. If the voltage stays high there but only drops at the relay socket(with the relay installed) then the problem is in the wiring or relay socket. Suspect corrosion on the relay socket first. Suspect the first 2 inches leading from the relay socket next. Wires rarely do not fail in the middle of the run unless damaged.