I seem to think that this was a tool for holding the scabbard straight while re-stitching the seams and for 'lacing' the mouthpiece and thinggy on the other end............. was it called a 'chape.....?
The old 60's Armourers shop at Knook Camp had one of these things still on charge before they moved the Demonstration Battalion to the then new Battlesbury Barracks. Nobody knew what it was for until I cleaned the old grease off it.
'Lacing' was the term used for fitting new retaining staples to the mouthpieces. Apparently, you put this mandril thing into the scabbard, spread the legs of the laces outwards slightly, fitted them in the holes and punched the laces in with a wood block. When the laces hit the mandril, they spread outwards and tightened and secured the mouthpiece and end thinggy
Never used one but saw a couple and Robbie Robertson told me how it was done. If it's all a load of rubbish, blame him!