I see from your bottom picture that there is a track mounted for something (maybe your slide). It looks like the screws holding this track are pretty evenly spaced and are likely being put into studs for the most support. Can you use those screws to figure out where your studs are outside?
On another thought - I had a bbq like this bolted to the side of a previous camper. Only used it once as the heat coming off the back of this BBQ scared the "HE double hockey sticks" out of me. I had considered making a holder using one of these Northern Industrial Tools Truck Service Step | Steps| Northern Tool + Equipment
and some angle iron but traded trailers before I could get it built.
Good luck in getting this mounted.