well, I run freshwater tropical, a planted tank, so it's light requirements are different than a marine tank's would be.
I run my lights 10 hours a day, from 11am to 9pm. The moon lights right now are actually manually controlled ... sometimes I turn them on, sometimes I forget. For me (and my freshwater fish), the lights are purely ornamental ... the fish don't seem to see very well in the dim blue light, and just take to their night time activities of sleeping. my pleco and oto catfish become more active, since it's now "dark" out for them.
I did have the lights on a timer previously, but I'm in the process of rebuilding my lighting, so things are a bit dismantled right now.
I leave the timing of moon lights up to the marine experts, as I have no experience here, nor do I know their effects on a marine enviroment.