IDK if you are in an apartment or a house, but one of the most common sources of apartment fires is a gas grille on the wooden deck.
Most complexes prohibit it for the reasons given, and do not allow grilling within 25' of the building. I do apartment / condo risk control surveys for insurance carriers and that is one of the questions they pointedly ask. They have the losses to prove how serious it is.
Things do happen...something falls over or flairs up resulting in a disaster.
Use a metal cabinet (an old rolling tool box comes to mind), and know that over time, it will probably get greasy as all get out. Grease on top of wood is just more to burn.