I would think the outer framework of the wall is probably 2x2. If that's the case you could do as I did and attach a piece a heavy plywood screwed into the framing. You can then attach the swivel TV bracket to it. I was even able to find stain with Close match.
BTW my TV is about that size and although I never weighed it, I would bet it is much more than 13#.
OK curiosity got me and I weighed it. 26#.
Better check your weights unless I got I really heavy one.
Ron & Charlotte
WD8CBT since 1976
32' Gulfstream Ameri-Camp & 05 Ram QC LB
I started with nothing and I still have most of it left
I never fail, I just succeed in finding out what doesn't work