First, you need to confirm that the switch HAS a hot and neutral. One way to wire a switch is to use a "switch loop" which doesn't involve having a neutral. Google that term if you want to understand what I mean.

Second, you can't just staple the cable to the wall. NM cable (which is what you actually mean when you say romex) needs physical protection. Either it needs to be behind the drywall or you need to run it in conduit.

You can run the wire in a "surface raceway", see https://www.homedepot.com/p/Legrand-Wiremold-700-Series-10-ft-Metal-Surface-Raceway-Channel-in-White-700WH/100144606.
You can get corners and boxes made to run the wire safely on the surface of wall/ceiling.

Right, should have thought about that, thanks!

And there is a code limit on how many wires can be in a particular size box: this is called a box fill calculation. So you need to research this to make sure you’re not exceeding the wire capacity of the particular box you would be adding wires to.

If what Greg says about the neutral (and ground) works, then I would break through the wall in the closet close to behind where one of the existing switches is and install a box and switch there, then run your wire up BEHIND THE DRYWALL to the ceiling and mount your light there. Forget the motion sensor.