Considering that the starter motor only pulls system voltage down to 9V, I am inclined to reject the idea of a high draw of the pump. I do think that there is a point of high resistance in the circuit between the relay socket and the pump. A loose fit of the pins in the socket, and/or corrosion in the sockets can do it. Next would be the connection of the wires to the bottom of the sockets, and then the terminal and post of the pump. Unless there is mechanical damage to the wire harness itself, a fault in the harness is a rather long shot. If necessary, a bypass wire from the 30 socket, run outside the car to the pump, can help isolate the fault.