The Tipton Cleaning Rod Rack is an inexpensive, easily-installed, wall-mounted solution to hold cleaning rods.
$8 at Midway. https://www.midwayusa.com/product/101491944?pid=653834
Downside: only holds six rods. Hooks on the ends can hold two more rods if they have loops.
The polymer plastic is pretty strong, though, and if, using a Unibit, you drill 1/2" holes between the existing slots more rods can be added and they all are accessible. Unibits are wonderful for drilling in soft plastic. Clean holes and no grabbing. And you can sneak up on the diameter.
The Rack can now hold 15 shotgun, rifle and pistol rods in the same space.
Obviously, long rods go in the original slots and short rods through the holes.