Don't laugh.
Promise?
Anyway.. I tried something extremely rough / quick & very funny looking out of two pieces of cardboard, a xylophone mallet, brown tape, rubber bands & two borrowed pencils from ikea (I will return them) only to see if it
could work i.e. open & close & write ! and it does. poorly.. but it does!.. just like a pointed pen! or more like my first 'pointed pen' that I cut out of a plastic bottle.
The problem(s) with this extremely bad construction was keeping the pencils aligned which is not at all surprising since I just pierced the cardboard & stuck the pencils inside, so, with a lot of pressure, they were pushed out of place. The card was also a little flimsy too.. especially after drilling through it in my hand with a screwdriver ..
Here is a pic just to show how 'simple' the design is. I taped the pieces of card together leaving the front end untaped so it can split open with pressure.. it worked better than expected & wrote thick - thin - thick - thin..

who's that laughing in the back?
Next step is trying a stiffer / snappier material (a thick ruler might work perhaps?) & finding a way to attach adjustable holders (such as those on compasses?) to hold the pen / pencil / chalk / whatever..