The pumps don't "prime".
The pump runs when the key gets to the "start" position.
When you turn the key back to the "run" position, the pump will carry on running if the ECU gets cam and crank signals.
Otherwise it shuts off.

You got that back to front.

You get vapour lock when the fuel pressure is too low and the engine is too hot.
That's the purpose of the fuel pressure solenoid, for hot starts.It increases the fuel pressure.

 

Probably not but I am not 100% sure. Just spitballing ideas from threads I come across.

The camshaft position sensor could cut fuel and spark too. https://www.evolutionm.net/forums/ev...on-sensor.html

 

I have done cam angle. I purchased a crank angle it is next on the list of install. To be honest I am thinking loss of communication with the keys immobilizer is making the most sense. Given the way it died and it's current behavior.

It's starts immediately with the initial fuel it gets, pump cuts immediately and car dies.

 

Sorry, I misread what you wrote then. You can disable the immobilizer to make sure that it isn't an issue. Just use Ecuflash to disable the immobilizer.