My 2012 Leaf had the same symptoms: EV warning light , P31E9 code, and whining sound. The sound was loudest on the driver's side which made me suspect that it was something else but the #1 water pump. I finally decided that it was the radiator fan going into high speed because it sensed that the pump was not working.
I ordered the pump on ebay. It was listed as a 215803JV0A or 21581-3NA0A. The price was $190 plus tax. It is identical to the one in the car except the mounting bracket is different. I took it out of the mounting (a rubber padding) by sliding it out. In addition to the new pump you need a small pair of channel lock priers and a siphon pump.
First, I disconnected the electrical plug from the old pump. Next, I siphoned the coolant from the reservoir above the pump. Next, I removed the two screws holding the reservoir in place. This allows you to slip the pump from the padding and lift it up to access the spring clips on the hoses. Do not remove them but slid them down on the hose. Notice that they have a marking across them that allows for setting them back in the same position to prevent leaks. Once the two hoses connected to the pump are disconnected, reconnect the hoses to the new pump and slid the clips back into place. Push the new pump into the padding, connect the electrical plug, reattach the reservoir to the body and refill with the coolant you siphoned out.
It took me about one and a half hours from start to finish. No more EV warning light and whining sound. I saved about $800 for my efforts.