1991 Ford Truck fuel system

maybe I don't under stand your post? Which pump doesn't shut off? It does shut off when you turn off the key?

The lite blue wire with orange stripe is ground for coil side of relay. If that wire is shorted to ground, the pump will run anytime the key is on. That circuit is grounded by the computer, when engine running, may have initial prime at key on, for a few seconds, without rpm signal the pump shouldn't run, except for prime seconds.