The gas cylinder plug unscrews from the front, and there is a wrench in the buttstock that is made for that purpose. Once the piston is removed from the rear, the gas cylinder can be cleaned all the way through using the issue pull-through swab.
Everything I can find, in German and English, indicates the short rod in question is a stacking rod, "Zusammenstellgerät" or "Zusammenstellvorrichtung", both meaning roughly "stacking equipment". It looks like the stacking rods used on many older rifles, like the Kar. 98AZ. I think it possible that the stacking rod was revived because of the muddy conditions being encountered on the East Front. (The K.98k has no stacking rod or swivel as such; the cleaning rods are used to interlock two rifles and then either a third is set up betwen them or two more are interlocked and set at a right angle.)