Cant help with reasons for the pump cutting out when warm unless you have it located inside the engine compartment.
I assume your car like mine started life with a Xflow engine & mechanical fuel pump & only acquired the electric fuel pump as part of its Zetec transplant.
The original loom did not have a fuel pump feed or relay, these will have been added, don’t assume these are in the original fuse box.
On my Zetec transplant I have an additional fuse box & bank of relays for the ECU, fuel pump & coil pack. No additional fuel tank breathing was added to my 1991 fuel tank.
Olly
the X Xflow