I put my jack and all tire tools in an old truck/suitcase that had a bunch of travel stickers on it. Bolted it to the floor in the back. An old wooden box would look good too. Looks like you are carrying "cargo" in your panel along with the tire. Tire covers are easy to make. One round piece of vinyl and one long rectangular piece sewed together.
Add elastic or a draw string.

Right is right, even if everyone is against it, and wrong is wrong, even if everyone is for it. - William Penn