Ygtjki

I have a built in area that is 21.5" deep (see attached picture). I'd like to mount a TV, but I've tried finding studs in the back wall and I think there might be one around the center, does not appear to be studs anywhere else as far as I can tell (and the wall seems pretty thin to the outside so I'm not even sure the "stud" I found is an actual stud). I drilled some tiny holes and the center is the only area that gave any resistance.

My plan is to add new wood to the area outside of the wall that I will paint white and attach a TV mount to that, does anyone know what size wood I should get for that (2X4 etc)? And also how would I secure it to ensure it can support a TV mount (aka put screws into the top/bottom or some specialized way to do secure it)?

Also if anyone has a better plan to mount a TV that'd be great haha, my plan is to get a TV mount that extends very far so the TV can be wider than the built-in area.

Thanks!

Edit: Added picture, whoops!
Edit: Thanks for all of the suggestions!! I'm an idiot and I'm going to start super easy and try a mount that uses a single stud, like this bad boy: https://www.amazon.com/gp/product/B00EVXEW7Y/ref=ox_sc_act_title_1?smid=A4RWQRCTJ6CYV&psc=1 This place was built in the 70's so I'm not sure what codes they followed - the stud finder "found" studs on the back wall, but I drilled a tiny hole into them and 2 of the 3 had no resistance (on the far left and right), feeling decent that the center is a stud. The wall seems very thin though so I'm definitely concerned that I'll go through to the outside haha, we'll see in time. If that does happen I like the idea of mounting plywood and using that as the studs, I think plywood glued/screwed in could do the trick, the TV is only 22lbs so crazy light.

Now that I see your photo I'd do this differently. I'd install a vertical cleat just behind the faceframe on each side of the cabinet, maybe 1" back (the thickness of the plate plus 1/4"). I'd then span a sheet of 3/4" plywood across them, creating a solid face on which to install your mount.

You should have either a cabinet wall or framing to screw into. Make the plywood as tall as possible without being visible to give it rigidity. You could also use two-by lumber if you prefer.

Plan view:

 | | | |
 | |_ _| |
 | | | <-- cleats --------------------> | | |
 | |_|__________________________________|_| | <-- cabinet wall
 | |______________________________________| |
 |_| ^ -- plywood plate |_|
 ________________________________________________
 / TV 
|__________________________________________________|

One advantage to this approach is that you can use a simple, inexpensive mount rather than an elaborate articulating arm mount. This saves money and results in a more stable setup. Be sure to work out the depth of everything so you're able to tilt as you like when you're done.

Original answer:

Rather than installing something that may be visible around the television, just add a sheet of 3/4" plywood to the one stud, and also adhere it to the drywall with project adhesive or silicone.

Cut a sheet that's about 6" smaller than the tv in both directions. Apply a 1/4" bead of adhesive to the entire back side in a zigzag pattern. Using four 2-1/2" gold screws, fasten the sheet to the stud Once the adhesive is set this will hold any modern tv with no problem.

Be sure to properly pilot your mount screws so they grab the plywood well. If you're using an articulating mount, consider installing a pair of toggle bolts at the ends of the plywood as insurance in preventing the sheet from pulling away.

Elevation view:

------------------------------------------------------
. .
. __________________________________________ .
. | * | . <-- TV outline
. | ( ( ( ( | .
. | ) ) * ) ) | <- . --- plywood
. | ( ( ( ( | .
. | ) ) * ) ) <-| -- . --- adhesive
. | ( ( ( ( | .
. | ) ) * ) ) | .
. |__________________________________________| .
. .
. ^--- screws .
------------------------------------------------------

No need to go through a lot of unnecessary structural changes. I would install a Base-Mounted Television Stand using bolt/nut/washer through the shelf. Depending on the size of the television you are mounting, you might even be able to store the television inside the shadow box.

Note: This particular stand will withstand 25 pounds. A Samsung 48" Smart Television weighs 24.9 pounds without the stand attached. You could cut a single 2x4 (tight fit) and place it vertically against the rear wall of the shadow box and install a few small "L" brackets underneath the shelf to prevent the shelf from giving in any way.

First you should probably get a stud finder they are supposed to be every 18" or so.

https://www.oneforall.com/explore/vesa-mounting-standard-explained#/step-1

Normally your TV has VESA mounting holes.

Buy any one of 1000's of VESA mounting kits from a store.

Affix the back plate to the wall.

Attach the TV to front plate, and connect the 2 plates however the manufacture says to in the manual.

I can't go into any further details because there are dozen if not hundreds of different designs for VESA mounting kits. You get the one that suits your needs.

You could even screw a 2x4 along the back wall into the stud, and then attach a VESA mounting kit to that.