Intermittent Start Issue with Crank - Goes away when Priming Fuel Pump

My 2007 SE X-terra (200,000 miles) has an intermittent issue with crank and no start.

I found, that priming the fuel pump (turn the key to start the fuel pump, wait 5 sec, turn off - do again and instead of turning off turn on the engine) will always start the car.

No issues at all once it is running.

There is no clear pattern.
The first couple of times I noticed this, it was a warm start issue - when the engine was very hot and I turned it off shortly, only to find it would not start up again.

Later this evolved into occurring maybe once or twice a week in all conditions.

I have no codes and a brand new battery.

First, I thought this is a fuel pump issue and exchanged the fuel pump.
After the exchange, I felt the car start up was a faster, and the issue disappeared - for 3 weeks.

Now the starting issues are back and appear intermittent again maybe once or twice per week.

I am quite confident it is not the battery.

Not sure about Cam or crank sensors

The car has the white IPDM!

Anybody any guesses?
Very grateful…