Can you check fuel pressure ? Maybe fault in tank pulling air ? Air in system would make noise could fit external fuel pump just too try feed from a petrol can they are cheep too buy
Not sure how close your car is to my 2004 XJR electronically. For the last year or so my car also often will only crank and not start. I put a diode on the fuel pump lead in the boot fuse block, so I can tell when fuel pump is energized. When there is power to fuel pump light goes on. I can see the diode as I taped it to my rear window!! Often when I turn on the ignition no light comes on. Car wont start. If I switch the ignition on and off several times the light will come on. Sometimes if I wait the light will come on after up to to about 12 seconds after turning on the ignition. Something in the car is “thinking” and disables the fuel pump. Could it be the fuel rail pressure sensor? I plan to replace that this weekend. I did replace the Inertia switch to no avail. Got fooled by the time delay into thinking this might be the problems. (long story). There are no codes on the OB reader, but I understand proprietary Jaguar software may tell one more than over the counter reader. No JAG dealer near me. Once the car starts it does not fail, except for once! Sometimes the light will go on for a second then shut off. All other systems on the ignition switch, such as seat belts, do not fail, so I feel is not the ignition switch itself.
The saga continues.