Truck Dies, unless I keep my foot on gas pedal

Has anyone asked if there is an aftermarket security system on this truck?
EDIT: Nevermind.... "remote start",
Yep there is.

 

The EFI NO. 1 fuses feeds 2 paths. It's the constant 12vdc input to the ECM at the BATT terminal. If that BATT input to ECM is lost, it affects the volatile memory....DTC's, Fuel trims etc

I say that to say, if hypothetically you have a periodic open in that path. might be why you're not seeing codes and the affects mentioned above....DTCs and current values for ignition timing, fuel trim, etc. IF that open becomes shorted to gnd, fuse blows.

As for the other path that the EFI NO.1 fuse protects, it sets at the input to the EFI relay contact pin 5. To energize the EFI relay, we turn key to IGN ON, relay energizes and thru now closed contacts pin 5 to pin 3, we now supply 12vdc to MAF, A/F O2 sensors BUT those circuits are protected by the EFI NO. 2 10A fuse and it should blow before the 20A EFI NO. 1 fuse.

I would consider replacing the EFI NO. 1 fuse with it's proper 20A fuse, pull the EFI NO. 2 fuse and the Fuel Pump relay. Attempt to crank and see what happens.
Finding a point where something is going to ground can be a hair puller.

edit....forgot to ask, does the 20A fuse blow if you turn key to IGN ON only ?

 

Well I wasn't 100% sure but having now looked at the 00 EWD, there is one for the 5VZ but not for 2UZ BUT don't let me stop you from looking for it....get you a 6 pack and have at it

 

I think you may want to check at some point if you may have water intrusion into the in-dash fusebox.

Or maybe the alarm as @BroHon alluded.

Often when we see multi-circuit stupidity in these trucks, it’s water in the fusebox. Multiple members hit by this. Multiple example photos linked in the sticky community mega thread.

But I’m not sure it explains the EFI-1 fuse popping.