My Cherokee is cutting out in a totally random pattern. Sometimes I can re-start it straight away, soemtimes I have to wait anything up to 30 minutes.

I have noticed, on quiet days, that a noise from the rear, quite like the fuel pump priming, immediately preceeds the ability to re-start.

If this is the fuel pump, can anyone tell me what is likely to "tell" the fuel pump to stop/start pumping?

Thanks.

Not quite sure were it is located but I would look for the relay that controls it. Go to autozone .com, and follow the prompts. That should help you a little. good luck. Also if you are stating to here the pump, good chance that it is starting to wear-out. The pump for my 00 XJ is about 200.00.