I have read through the answers and tutorials, but can't find anything that deals with time-based progression.
This post contains a count-down. Can this be used to trigger other events? It seems like a case of 'when time=0 do y' or something, but I don't know Java or Unity well enough to write it myself.
Additionally, I don't want there to be a visual timer, but rather tie the time into a) the movement of the main light (to replicate the passing of a day) and b) into brief cutscenes for the 'night time' animation. (I'm also working on how to do 'fade to blacks' as a fall-back)
After a handful of these day cycles, I'd like it to end in another cut-scene, dependent on items found during the game.
I'd appreciate any advice or suggestions you may have. It's for an assignment, so I just don't have the time to go away and learn Javascript well enough to make it myself. :S
Unfortunately you're going to have to learn Javascript or C#, since we won't code for you here.
I can give you some suggestions, though. First, you might want to look at Coroutines, as many people use these for sequences of events (things like cutscenes, time-based events, etc).
As for creating a moving sun-like entity, you could just have a Directional Light in your scene, and then rotate it accordingly, creating a sun-like effect. You could even change its color over the course of the day to go from an orange-like color at dusk/dawn to a bright yellow during the day.
And you shouldn't use that timer that you specified... it puts the timer countdown math inside of OnGUI() instead of Update(), so if you don't even want a GUI for your timer, that would be somewhat useless. It would be much better to put it in a coroutine or just in Update().