That resistance your feeling 1.25" deep is probably the skin on the opposite side of the wall, as that is typically the wall thickness.
To find the nearest stud I use the tried and tested age old method I've always employed.
Apply pressure with your thumb along the wall where you want to hang the TV. You should feel the thin 1/8" wall board flex pretty much wherever there's NOT a stud.
When you find a rigid area, give it a tap with your knuckle and listen to the pitch. Move left and right across the area repeatedly knocking, you should hear the pitch change and sound more hollow as you pass unsupported areas.
Once you find the highest pitch point nearest to where you want to mount your TV, run a thin, no more than 1/16" drill through the board, you should feel your stud. If you miss it, move left or right in 1/2" increments until you find the center of your stud. The TV mount base plate will cover the little holes you've drilled, if not it's time to get out the spackle.
Good luck, AND BEWARE, don't drill into the A/C wiring, plumbing or propane lines.
I've got more holes in my walls than a Swiss Cheese....Hee hee. Only kidding
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