Yes, it works with the zaxis, and needs a rubber band at the end of the pen to provide some tension. I made an improved and simpler version:
It has one fewer side support and much simpler finger joints. The zaxis fits between the top two pieces and allows it to control the height. It does still need a rubber band. I was just going to attach them using some screws on the top.
The fusion 360 design is here, be sure to look at the user defined variables and at least adjust your stock thickness: