Gun cleaning rods stored externally usually had a canvas or leather draw-string cover for the bore brush/swab. So the "wood" color being recommended by the paint/finishing guide is likely trying to steer you in that direction. I normally paint mine using a "field gray" color to simulate a canvas cover as a personal preference.
As the others have mentioned, German gun cleaning rods are typically wood bodies with steel ends that were threaded and male/female ended to allow them to be joined together into a single long staff to clean the gun. Late-war staffs were also sometimes made out of Bakelite (an early type of plastic) which would give them a dark brown or even black appearance depending. HTH!