I was thinking of doing this, not for a reverse monitor, but for a monitor displaying sat nav and other media (music)
I had a measure up and i was considering attaching rails to the sides, but the back of the compartment it a lot narrower than the front
So in the end I decided on a runner mounted on the base of the compartment with a sprung loaded hinge to flip the screen up, and then a small knurled bolt to clamp the runners while the screen was out
Decided it wasn't worth the effort in the end lol