It seems like such a device might better be handled by just making a schedule for yourself based on data about the seasons and moon cycles, etc., finding the values that need to be put in and the dates that the timers need to be changed for those values, and tacking that schedule to a wall. Perhaps there is some internet resource that gathers and coordinates these details to tell people exactly what the light source is and is going to be in one place or another every day of the year. I don't know enough about climates to know if that sort of thing is possible or not.
It may be likely that in the future there is a very flexible timer that can be programmed very finely by an app, or an app that includes dates throughout the year and the time periods for each date to have the power on, or even a timer that outright coordinates power with the latitude, moon cycle, weather, seasons, etc. (Actually, the first 2 of those 3 may already exist, and I just don't know it. I don't think the third one exists yet, but it's hardly unrealistic.)
Like jgragg said, though, if you aren't after ultra-realistic settings, but just want the plants / animals inside the box to survive, it's possible already to do that.
But it's a good question to ask.