> But why haven't deer or bunnies, for example, evolved to have white patches on their rear ends
They have. Bunnies famously have distinct white tails that bob up and down as they run.
http://blogs.nature.com/news/2013/08/why-rabbits-have-white-...
And some deer have distinct white/dark patches on their backside:
https://krahnpix.files.wordpress.com/2012/09/t6c8813.jpg
https://i.imgur.com/6JZdQBz.jpg
The article conjectures that the function of these is to be a super-salient signal for a predator's visual system, so they attend to the wrong end of the prey in a chase. Maybe tracking the back end gives a degraded cue to the predators prey-motion-model. But the high-contrast patches are hard to ignore, like chaff for radar.
This is probably a different effect than false eyes have on cats, since cats sneak up on prey that aren't looking.