I'd try 3-inch wide blue painter tape, attached underneath the desk. When pens fall, they'd only be a few inches down, the thickness of the desk.

get a decorative pen holder.

What's causing the gap? i.e., is it the baseboard or something else? is this wainscotting or just a chair rail? there might be solutions, but need to understand the problem better.

You could get a 4" wide piece of trim molding cut to fit, finish to match the desk or chair rail, and shove it gently into place next to the wall. The ideal trim molding would have a pencil-width indentation, like wooden desk drawers used to have inside.

I have same issue and found something on Amazon. But it's ugly. I'm having a woodworker make one similar for me.

Stain a thin wooden plank, the size you need, the color of the desk, and attach it to the surface of the desk with double sided tape.

https://www.thingiverse.com/thing:3328125