You are thinking that instead of magnet, you’d have the LED? That would work fine.
The UV LEDs I’ve seen do work pretty well, but as Barry said, after a minute, they are tough to see, and it has to be pretty dark. Any other party lights would drown it out.
If you wanted to do this, I would start very small, like 8"x8", so that it could draw everything quickly. I would start with patterns that looked good even if they weren’t 100% finished, like geometric things. If you draw your mother’s face, some of it will be dim before it’s finished. If you’re drawing stars, then some might go out, but so what?
The next step would be controlling the LED with gcode, then you could essentially “lift” the pen and draw independent objects.
I think this is a great idea and you should try it.
I know this thread is a year old, but I built this project which would give you a good idea of how it would work. (The video is not of my finished project, but of the someone else). https://www.youtube.com/watch?v=-MnolVyKqvo.