Mines a 2002 zx6r with 49300 miles on it been in the garage 4 6minths started every so often did the mot (£600 later) past it rid it home great next day started doing this. I work for the nhs and it's mean own way of transport so needa fix asapMost of the pumps I've read about you can hear them priming..more so if it's an aftermarket version.
Also check the t-bag filter/fuel strainer inside the pump assembly.. it can cause the problems you're experiencing similar to fuel starvation..
Just be careful when you pry it apart and take note of the wiring..
I thought it was my fuel pump but alas.. still does the same thing with a new one