You certainly can leave the lights on 24/7 but then you may be dealing with light spilling over into the main tank. Also, chaeto won't go sexual if not lit 24/7, plus it would grow just that much quicker than it already does, so I choose to light mine only while the tank lights are running.
Ben, I didn't mount the brackets on the outside, because the sides of the media basket have tabs on them. I cut the tabs off, but it wasn't a flush cut and I wanted to be sure I got a good bond between the brackets and the sides of the filter. You can modify it anyway you see fit.