I don't know if any advice I offer will be any good at all because I took a look at a Chiltons schematic. Anything from Chiltons is always suspect as to accuracy. However, proceeding on....
The voltage reading at the orange wire should be battery voltage; 12 volts. Test this with the relay out of the socket.
The gray wire is to the pump of course.
If there is a dark green/white wire at the relay socket there should be voltage there for 2 seconds whenever the key is turned to the RUN position without energizing the starter motor. Without cranking the engine over that voltage will disappear after 2 seconds but if the engine is then cranked over the voltage will remain and keep the relay energized.
If there is a black/white wire that should be a ground for the trigger part of the fuel pump relay.
In other words, the dark green/white and black/white complete the circuit for the trigger part of the relay.
If power is not provided through that dark green/white wire in the situation as described above this could point to a problem with the electronic ignition (no pulse to the ECM) or a fault with the ECM.
An ignition pulse must be present to keep the relay energized and yes, a crank sensor could also be the cause.
Automotive fuel systems are set up like this to conform to Federal laws which require the fuel pump to shut off on a non-runnng engine in certain situations; say an accident.
Hope some of that helps anyway.