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When I had to do that I could not find anyone selling a 5/16" square bit. I cut a piece of 5/16" square stock steel into several 1" to 2" lengths and welded them into some extra 3/8" drive sockets I had laying around.
I make sure to keep one behind the seat along with the block drain plug I pulled out when I installed the coolant bypass. With my luck, I know I'll be in the middle of no where when the hose blows and I want to reinstall the block plug.