Find the studs is the best way although not all that easy to find since they are often only 3/4" wide. Sometimes a cool morning you can often see the outline of the studs on my trailer.
My personal take is to NOT add anymore places for water to leak in at, I would recommend skipping attaching stuff to the sides and you will be happier down the road.
I personally would not like the work of cleaning the side of my trailer after cooking. Grease tends to splatter everywhere and having a grill hanging on the side of your trailer is nothing more than an invitation to scrub down the side of the trailer.
I use small aluminum portable fold up camping tables (2ftx2ft found in the camping section at Wally World) , place the grill on that and place the entire thing at least 6 ft away from the trailer side. It took me only once cooking right beside the trailer to realize that it was not a good idea.