The approved New Mexico fix is to flatten a tin can and nail it over the hole.
LOL
Yes, having spent a good deal of time in NM I’ve seen that fix.
Usually the nuthatches carve out a half dollar sized hole but they
found some soft wood and made a 2”X8” wide gash in one spot.
My temporary fix was a piece of half inch mesh galvanized screen.
Smaller holes have 3”X3”X3/8” plywood covers either awaiting repairs or protecting the patches until they cure.
Very Dog Patchian. ;-)