I hand sawed a piece of brass rod that was similar size to the hole, then used a sanding disc to sand flat, but it could be sanded flat with just a piece of sandpaper sitting on a table.
Depending on your brass rod, you may need to drill out the hole just a tad. Other than that, no big tools needed.
Suggestion, instead of doing a single brass rod, make 2 small ones. That way you don't have to have the exact size rod and sand flush. You add glue in the hole, then push it in until is sits flush, then do the same on the other side.