Going back to similar old designs it's not the chain making the noise it is a mechanical clicker or clacker like a peg on a bicycle wheel spoke that makes the noise to indicate trim wheel rotation.
Under the pedestal is a brake arrangement so that the pilot can arrest stab trim runaway. If one of you sets the stab trim trimming, then the other can pull on the control column and the stab trim stops with a big clang. It is this mechanism you can hear.
But please don't break it. I once spent a weekend changing a stab trim control cable. There are only two of them. It is wrapped around a big drum at the front about 40 times, then goes back through the floor beams and is connected to the rear drum. One single cable. The second is wrapped around the rear drum 40 times and attached to the fwd drum. It was not a pleasant experience. Every time you got it correct, it moved and all the turns fell off the drum!
Glad I work on Airbusses now.
