I had something similar in my Outback travel trailer in the bedroom. I figured out there was a board placed horizontal between the wall studs and that is where the screws needed to go. I figured this out, because I used a stud finder and was able to outline the shape of the board. If you have a stud finder, that will be the best way to find the supporting board and get it's dimensions.
It's been a while, but I think mine was about 8 inches (up and down), and the length between the studs. Not real forgiving, but the kind of wall mount I used, it worked fine, because I attached a bar where the other half mounts to the television and it can be lifted off at any time. I never traveled with that television on the wall.