I can definitely hear (or not hear) the fuel pump when it does or does not come on. For the past couple of days the truck starts and runs 100%. One thing I did think to do was to pull the fuel pump relay, and then try to start the truck with starting fluid down the throttle body. That did not start the truck, so that makes me feel better about it being a fuel pump issue, as it was that experiment from my OP that had me questioning whether it was the fuel pump. I think I'm going with fuel pump. So hard mentally to replace this when the truck is running great.
You've completely lost me there. You expected the truck to start with the fuel pump disabled while using starting fluid and because it didn't, you are suspecting the fuel pump? Does not compute and especially with a fuel injected engine.
I have no first hand knowledge of how Ford does things but so much is common between car manufacturers. The pump should come on at key on, run briefly and then quit. When cranking the pump should be running and then obviously stay running if minimum oil pressure is reached within x number of seconds. If not, the pump will stop and the engine will too. Ford uses an inertia switch in the FP circuitry that kills the FP if the vehicle is in an accident. As far as I know that's unique to Ford. Are they problem children? I don't know but it may pay to find out. From what I can see at the RockAuto site they are used on their trucks but I don't know what engine you have to know for certain. I am also seeing mention of fuel shutoff solenoids so there are a number of components that make up the fuel system.
Throw parts at it if you wish, it's commonly done. But dropping the tank to replace the FP on a whim is not something I would do but to each his own. One thing is for certain. If you throw enough parts at it, there is a huge chance that you will eventually fix it.
Is there an identical relay that you can swap for the FP relay? Quick way to tell if you have a flaky relay. I'd swap the relay first. If that doesn't take care of the problem I would be trying to determine if current is actually reaching the fuel pump at key on which I know is going to be a toughie because sometimes the pump runs and sometimes it doesn't. So first, get under that truck and start unplugging the connector or connectors that lead to that fuel pump looking carefully for signs of water entry or corrosion. Try to trace those wires back towards the front as far as you can get unplugging and checking connectors as you go. You have an intermittent problem which has electrical problem written all over it. I'd also be trying to get my hands on a wiring diagram. I'd be doing that because I have no firsthand knowledge of how Ford does these things. What would also be handy would be a troubleshooting tree for your exact problem which would be "intermittent no start condition".
And I get it, intermittent problems are very difficult to diagnose and even more exasperating when it's an intermittent no start condition. But personally, I never see throwing parts at a problem as a solution. My opinion is of no help to you, I understand that.
You should tell people here the mileage on the truck and what engine it has. I think that could help people to help you. Your local Ford mechanic might be willing to give you some guidance for a six pack of beer. It might be worth trying to get in contact with one. For all you know you may have a common problem that he can tell you with near certainty what the problem is just from your description.