Fuel Pump cycling

I'm running the engine from an '84 GPz1100 with an aftermarket fuel pump. When I first key on, the pump comes on, pressurizes the system and then stops untill I crank the starter. From what I understand this is the correct operation of the pump? After a ride, if I turn the key on again the pump starts cycling on and off until I turn the key off again. Is this a common issue? I thought it may be heat related with the relay either due to the proximity to the engne or from running an aftermarket pump (can remember exact model but it was recommended here in this site somewhere)which may draw more current? I installed a heat shield but that didn't seem to help. Any ideas for the cause for this?

Your fuel pump relay controls the pump operation. I suspect possible dirty contacts in the relay, or corroded ones in the fuel pump connector. Check the return valve(the one screwed into the bottom of the tank), if it's sticking, it can affect pump operation too.

I have done a load of research into fuel pump relays and have found this one from AutohausAZ.

W0133-1615089

Bosch
Fuel Injection Combination Relay

I have purchased one and it initally seems to work. It runs the fuel pump for about 5 seconds when the key is turned on then stops. Then when the engine cranks over the fuel pump comes on continuously. I haven't run it for more than a minute, as yet. I found that the real issue with my bike was the pump itself.
Not sure how or why yours cycles when hot. I am pretty sure it shouldn't do this.

The Bosch Double Relay would be a great choice, thanks for posting the part # NZGlen.
I'm sure the pump should run and not cycle on and off once running, hot or cold.
I'd check the control side of the relay, that is the power and ground circuits for closing the electromagnetic coil in the relay. Make sure the ground there, and power is constant.
Check all of the ground connections for the wiring harness, especially where it bolts down to the engine.