The OP's question was about the orientation of the mirrors of a light clock. I noticed that my app (https://joekahr.github.io/lightclock/) had a bug that made changing the orientation difficult. It's fixed now.
I also made the Center Clock default settings more intuitive: clock is moving in...
OK. I am here to learn. What did I get wrong about the physics?
Perhaps you object to not showing the light clock in its own frame when the Center Clock option is set. I address this in the FAQ under "Why does the Light Clock stay contracted and its time dilated when 'Center Clock' are...
I wrote a light clock app (https://joekahr.github.io/lightclock/) that allows the user to change the orientation of the mirrors. Please try it. Comments are welcome.
I have written a Javascript/HTML5 app that simulates a Light Clock as a way to understand the kinematics of relativity. It shows special and general relativistic effects, and how they are related. I would appreciate any feedback on the app, it's correctness, and it's usefulness as a learning...