If the diagram from the link is correct (I’m not saying it is!) then you should have a definite ground and power +12v, with your signal running to the ecm.
There is a fuse that supplies power to this sensor (check that first, although I would think there would be other things missing if the fuse was bad, but just to know ,check it anyways).
With the fuse removed, you should likely still see your 2.5v on both signal and power pins because I believe it is coming from the pull up resistor embedded in the ecm circuitry.
If you believe the circuit diagram is correct, you could run a wire from the fused side of the circuit to the connector , back probing would be easiest (likely) to get power to the sensor cable. You Need To Verify That Connection Should Be 12v!
If your willing to trace the wiring then use your ohm-meter to check for continuity, this will be difficult without a schematic. As well verify the pins on the connector are in good shape and no corrosion is present.