Will not start when hot

This sounds like a crank sensor has failed. Here are a few guides that will help with this in figuring out what the issue is:

https://www.2carpros.com/articles/symptoms-of-a-bad-crankshaft-sensor

https://youtu.be/dCjmRL3p4Cs

https://www.2carpros.com/articles/crankshaft-angle-sensor-replacement

Below is the process from the manual that shows more info about this as well.

I would replace this and retest to see if it still cuts off. Let me know if you have questions. Thanks

You are right. That doesn't sound like a crank sensor however, it may be running off the cam sensor and then when you cut it off, it starts back on the crank sensor.

Does it crank normally when it is hot and not starting?

If so, we need to check fuel pressure and for spark when this is happening. We need to find out which we don't have so we can track that down.

Okay. I understand. However, we need to find out what we do not have when trying to start the engine when hot. Just listening for the fuel pump is not going to be definitive because if the fuel pressure is low it will have trouble starting the engine especially when hot but it will be able to sustain the engine while it is running.

When the engine is hot, try using starter fluid in the intake and see if the engine starts.

If it doesn't then try performing a clear flood start by holding the accelerator to the floor and start the engine. If it starts while holding the accelerator to the floor then that means you have leaking injectors and it is flooding the engine. Holding your foot to the floor will cut the injectors off while cranking the engine.

Lastly we need to pull a spark plug when the engine is cranking and see if there is spark.

Let me know what you find with these three things as we need to start testing things to narrow it down. Thanks