You obviously have a loose electrical connection somewhere. One way to find
this is to sit down with a complete wiring diagram and go through it until
you find one spot that affects all these circuits. This can require a fair
amount of electrical knowledge because sometimes a misbehaving circuit can
affect adjacent circuits. A good electrical technician has the best chance
of finding it.

But your dealer is being honest. They pull their hair out about these things
since they can be so hard to find.

I have had a couple of vehicles in the past (not Ford, but this can happen
anywhere) that you would swear were inhabited by aliens. They kept running
so I just ignored the pings and warning lights.