Maybe left field but you could have an hdmi switch between you bt box and the tv. One output goes to main tv and the second output through the wall to the second tv. Input from the bt box. You can get standard hdmi to micro hdmi cables to go through the wall if needed, then a converter back to standard hdmi to connect to your second tv.
Use an ir extender if needed as above.
Works for me
Thanks for your comment.
I have an HDMI cable to the 2nd tv but through a powered splitter rather than a switch. What would a switch do that a splitter doesnt?
Usually a switch = splitter in common parlance. Others will tell you of the difference. But if you have a splitter that shuts off one TV and switches on the other then it's a switch. If not then it might be that the signal is unable to service both TVs