[I used to run my refugium light on 'reverse-lighting' which would be on when the main display was off. Caulerpa grew nicely, but several times over a period of a few months, it would 'go sexual' and die. Changing my lighting to 24/7, it never did that again, and I stopped having to buy more of that plant.
Cheatomorpha can be in darkness without a problem,btw.
Reverse-lighting is designed to help maintain pH. pH drops when your main lights are off, but the refugium can bring it up during the late night hours.]