It's a remixed mash-up of "Brass Neck" and "Mr.Quicke Cuts The Cheese", from "A Recipe for Disaster" by DJ Food. I assume the person who prepares music for David Wilson's clients was the one who edited it, as I haven't heard it anywhere else. It was always called simply "Rooster" on the list of Nobunari's programs.
Oh, and his "Super Mario" program was skated to "Super Mario Bros 2 Super Buck Jazz OC ReMix" by Estradosphere. (Also edited a bit.) His Mission Impossible LP was from "Mission: Impossible III" by Michael Giacchino. His 2012-13 SP was actually "The New Moon in the Old Moon's Arms" by Michael Kamen.