Intelligent Design: Irreducible Complexity?

[Esquilax]

How did photoperiodism and daily synchronization of circadian rhythms develop before eyespots came along?

So you ask a question about the development of the eye, and then when the answer is given your idea of a rebuttal is to ask me a question about things that happened before the development of eyes began, as though that has any bearing at all on the question you initially asked?

Unfortunately a search on evolution of eyespots (the first step on the journey) mostly turns up pieces on false eyes on butterfly wings. Here's one that's on point:
http://www.d.umn.edu/~olse0176/Evolution/bacteria.html

Now that random mutation is understandable, imagine a population of plain, primitive bacteria (no specific size, shape, etc.). There are trillions of them scattered throughout the world. Imagine that one out of every million of these trillion bacteria experience a mutation which allows it to have a pigmented surface. That means we have one million bacteria with some kind of a light-capturing surface on them. A few out of these million bacteria develop the pigmented spot over an opaque surface connected somehow with the rest of the internal network of the cell (Patton). These few cells, have just developed a primitive type of vision.

The irreducible complexity problem is just blown off with a single sentence.

Because it's not a problem: as demonstrated by the very thing you quoted, the eye is very clearly reducible. What's your contention here?

I could have a light sensitive cell on my elbow, but it's not going to do me any good, as the rest of my body either doesn't receive the information it provides, or doesn't know to do anything with that information.

Yes, and if the light sensitive cell isn't also connected to an apparatus for interpreting the information it receives, then it doesn't confer a survival advantage, but it also doesn't confer a detriment, really. Which means it persists in the genome, until eventually it does find a connection to the rest. That's the whole idea of natural selection.