It sounds just like a dicky relay, I think on these there is a relay on the n/s inner wing for the pump control, but not familiar with these at all.
It is most likely the vibration of driving keeping the relay working or the pressure is rising falling if duff and just not bad enough yet to notice the lowering fuel pressure.
It will cause absolutely no harm running constantly like a efi version, as it is regulated anyway.
You could try a new pump relay if you want.
tabetha