Remove the Fuel Pump Relay and turn on key, see if fuel pump stays off
If it does then the Light Blue/orange stripe relay wire is Grounded which it shouldn't be.
This wire runs to 2 locations, pin 22 on the computer connector, and a slot in the OBD I VIP connector, it is on drivers side engine compartment.
Look here for what it looks like: Ford Ranger - Testing EEC-IV Equipped Engines
Drawing there show which slot is the Fuel Pump test slot.
Make sure no one has put a jumper wire there, if you Ground that slot fuel pump relay closes just like the computer would do when engine is running.
You can use that slot to test for ground on the light blue/orange wire
Disconnect battery's negative cable
Set OHM meter at lowest setting, put one probe in that above slot, place other probe on a good Ground.
0-1 ohms means blue wire is grounded, it should read high or N/C(no connection) if wire is as it should be, not grounded.
Disconnect computer, in case pin22 circuit is the issue
If ohms change to very high or N/C then computer circuit is the issue, new or not.
But I doubt it will change, if it does then check the pin22 blue wire on the connector and follow it as far as possible, short to ground could be near computer connector and when it was remove the ground was lifted.
Start tracing the blue wire(from VIP connector and fuel pump relay) and move wire around, see if you can find a place where ohms change, i.e. the bare spot where it is touching metal or a ground.