Yup
If a wiggle test caused the pump to prime you have a bad connection in the relay ( edit and or fuse) sockets. Hard to find by eye really, but basically the lugs are opened too far allowing the relay to slide in without making metal to metal contact. You can remove each lug one by one to close them up a little but be very careful, as too tight will cause the lug to push out the back of the panel when the relay is inserted.
You can also try slightly twisting ( very little, maybe 2 degrees) the pins coming out of the relay which will make them scrape into the connector lugs better. This one fix allowed me to drive home from Colorado when I was actually preparing to drop the tank at a campsite.
edit. don't forget the PCM relay and fuses. If the PCM has no power the fuel pump will not prime.
when doing wiggle test try less aggression to the wiggle. Try to move them one at a time to determine which exact wire's movement causes joy.