I am pretty sure that those pieces are not real wood and are just plastic that looks like wood. I would also stop using Armour All as it is not a very good product. I would look at something more like Meguiar's Quik Interior Detailer or even 303 Aerospace Protectant. Both are great products and will leave a nice satin sheen on the surface. Hopefully this is helpful for you.
KMG has a point tho,...... armour-all bein white in its liquid form, hence when the sun pounds it it tends to hve a washed out n sun bleachd look, plus it will dry rot tires more so than other products. Try usin a clear based product. Blk magic perhaps.
There are much better dash and plastic cleaners. To clean up your woodgrain of grease and finger prints, you can actually use window cleaner on them without leaving streaking. You can also wax/seal them to give them some uv protection.
But my go to interior product is 1Z's Cockpit premium.
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