Should only prime with the key to IGN, not ACC. But anyway, what you need to check si whether the relay clicks every time but the pump doesnt whirr every time, or whether the CO relay only clicks 2/5 times and the pump whirrs every time the relay is heard clicking.
That will tell you whether it's a wiring issue in the key barrel/main power area or whether its a pump or at least wiring to the pump issue.