Fuel pump stays priming

[redcar]

Hello all, developed a strange problem with my m52 converted e30. Car was originally a 316i m40.

- When turning the ignition on the pump is just constantly running (rather than priming for a few seconds and switching off)

- The car only starts after around 10s of cranking and pressing the accelerator up and down.

- When the engine does get running it seems a bit down on power and I think it's misfiring slightly at around 750-1000rpm

- Compression test is 11.5bar on all 6 cylinders and I'm getting spark at the spark plugs also

Any clues as to what could be the problem and any tests I can carry out to find the fault? I'm thinking injectors or fuel filter related?

Thanks in advance.

[DanThe]

ECU controls the initial prime and the running of the fuel pump, faulty ECU or relay would be the first things id investigate

[redcar]

So these problems I've described are isolated to yesterday when I was at a track day. Obviously car was very hot and I'm assuming that's related, as I just went outside today to start the car and fuel pump primed for a couple of seconds and car started up immediately and runs perfectly, making all the power.
Any ideas? Need to solve this soon as got a nurburgring track day next month.
Thank you

[redcar]

I've done some googling and my signs point towards it being a crank sensor.
I think I have a spare one around so will fit that see how it goes. Not sure how to test these though as the problem only occurs on track when the engine is very hot.

I'll scan the fault codes and inspect the current crank sensor for any damage.

Even if the problems aren't actually present will I still get a fault code if the crank sensor is dodgy?

[redcar]

Please could I have some help before I get round to changing the crank sensor?

Am i heading in the right direction or barking up the wrong tree? Not sure what else would cause hot start issues where the pulp pump remains priming when the ignition is on.