4.0 in an 03 Explorer, E code, 112k new to me. Just a parts rig but it's in better shape than my winter-beater, I might just start driving it..?

I took it for a test drive, ran fine. No startup rattle, good lookin oil, etc. No lights. Took it for a spin, everything is fine.

Picked it up a couple days later, start fine, load on th trailer, fine. Take the battery out (not included) and tow it home.

Put a battery in at home, start er up, throw it in gear, drive 50 ft n it dies, starts right up n 3 secs later dies, start, run, die, repeat. I can tease th throttle n get 2k rpm n then dies. Almost like a time limit is reached n then it dies....

Is there a driver that powers th fuel pump after the initial 3-5 seconds? Does it rely on engine oil pressure to signal the fuel pump relay to stay on? Power steering pressure? Alternator voltage?

I was told they replaced the fuel pump, but looking at the yard, no garage, I'm sceptical. I have a cheap fuel pressure guage coming from Amazon so maybe my question here is premature.

Any guesses?

 

Ranger didn't have a fuel pump driver, not sure about explorers, F-150 did, and loads of problems with those