Wood – Sanding, staining and varnishing wood, outside

It sounds like you have solid 13/16" thick plywood for a wall. If that is the case, I'd drill holes matching holes in the mount all the way through, get four metal bolts, four matching nuts and eight washers, and hang the mount on the wall, securing with nuts from the opposite side of the wall and using threadlocker on bolt threads. You would have nuts permanently visible on the back side but the construction should be more than sturdy enough to hold a 40 lb TV.

If you don't have solid plywood but something else (I doubt that there's enough room for anything else but who knows?), that's a different story. You should find out as soon as you drill the first hole.

I have found that wood conditioner is unnecessary for harder wood species. The primary purpose is to help reduce blotchy spots due to uneven stain penetration, which in my experience is prevalent with soft woods.

Previously finished woods may be less susceptible to blotchiness, depending on how thoroughly the wood was sanded. Conversely, less than complete removal of existing finishes can itself cause uneven stain penetration.