Fuel pump issues.

Is that when the trouble started? Because that is what the inertia switch is for, a bump to the truck can definitely cause the switch to trip, maybe it only partially tripped, it kind of like a circuit breaker, if it gets tripped you just push the button on top and reset it.

Looks like a north carolina vehicle.

This is inertia switch and reset button, give it try.

Yup, thats the switch, if you pull the carpet away a bit you will see the connector and 2 wires on the bottom of it, with these if I need to check the switch for whatever reason, Ill just keep it simple, I will check the voltage level on the Dark Green wire first, then check for the same voltage level coming out on the Orange wire. Most of time you can do this without even having to unbolt the switch, although that will make it easier, but I would grab a cheap multimeter somewhere, (walmart, autozone etc). You just need to read DC voltage and resistance in some cases (Ohms). So you can get a cheap meter probably for $20 or so, and this is Harbor Freight's cheapest fuel pressure gauge that does come with the Ford adapter, its the most common adapter out there.

In this case, since we really dont know if that inertia switch is ok or not, you can do a couple things here, you can unplug the switch and jump the two wires together, just make sure youre using the same or higher gauge because the fuel pump pulls some amperage.

You can also do a voltage drop test across the two wires while its plugged in and the pump is running, you should read close to 0volts, meaning there is no voltage loss on the switch itself. This is very basic testing, so dont let the terminology get to ya.

I would do the testing first before jumping the switch out, unless youre comfortable doing that, it would eliminate the switch altogether for now. But seeing what the fuel pressure is doing is important, this might be something completely different than we think, so its very important we test so we dont change parts that dont need to be changed. That gets expensive.
HF has a meter for $5, cant beat that.

So the truck wont start even when you hear the pump still running? I just want to make sure we're on the same page here.

Read through this guide to get an idea on fuel pressure testing. You basically just thread on the pressure gauge and key On first, make sure it gets up to 40-60psi. Put a shop rag around the fitting when threading it onto the fuel rail, some gas will come out, so we want to make sure theres a rag there to soak that up. Make sure its threaded on straight and down all the way.

https://www.2carpros.com/articles/how-to-check-fuel-system-pressure-and-regulator

That happens even with the new pump in?

I guess what I was really asking, is do you hear the fuel pump running when the engine wont start?

Ok, thanks. So it is possible we have more going on here than just fuel pressure. But it should still be checked and monitored while testing. These trucks only have a couple control modules in them, they are not super complicated.
It sounds like its heat related then, which could be any number of things, but we'll start with getting a pressure gauge on the rail so you know what the pressure is reading and can watch for any changes.
You have one of these 12v test lights also? I would pick one of these up as well if you go there. Just because I know the current flow for these test lights. I have a bunch of different test lights that all pull different amounts of current for whatever I happen to be working on. Some circuits can only take so much, especially when it comes to what the PCM can control.

The spec is 35-60psi, but I like to see them at least above 45psi, but since you do have a test light, you can still see if theres power at the inertia switch if you can get the truck to fault pretty easy. I think youre going to find there is power. If that pump is running,
Did you have to drop the gas tank to do the pump? I just take the bed right off the truck, its only 6 bolts and the whole thing picks right off the back, you'll need help but its much easier to do testing and/or swap a pump out, no need to drain the tank and drop it at all. I had to do a pump in mine not too long ago, and it was really fast that way. The 6 bolts are large Torx bolts, you can see them right in the bed.

Yeah, you wont be able to see what the exact voltage reading is, but make sure the test light is bright on both wires at the inertia switch. You can do the same for the connector at the fuel pump, put the test light in place the of the pump, that will help verify it has good power and good ground. The test light doesnt pull much for current at all, but its something you can check in the meantime.

You did get this guide to checking the fuel pressure too when you can?

https://www.2carpros.com/articles/how-to-check-fuel-system-pressure-and-regulator