Yes you can rotate it for any position between the dots and it will stay fine. Just turn the laser on and line them up horizontal to each other and you will be good to go. Just check it once in a while to make sure you haven't bumped the lens one way or the other while turing it on and off.
My set up was on the right side until i found myself wanting to keep riding and turn on the camera at the same time. I would have to let off the gas to turn it on. I have found that I like the left side better because I can turn on and off the camera better on the move with the left hand. Just something to think about. I have had it on the top, on the right and the left. I like the left the best because I can be heading up the hill and then decide to turn the camera on without having to let off or reach around with my left hand to the right side to turn it on. My recommendation is left side cheek below the googles.