The idea of pure random behavior is critically wrong in understanding evolution.
This is very poor wording on your part. "Bahavior" is arbitrary, or is governed by rules, and is never random. Hence, there is no such thing as "random behavior." It is a contradiction in terms.
Otherwise, Darwin's theory of evolution is based entirely on random occurrence of events.
It isn't just throwing up the pieces of a Mazerati and getting one fully assembled. Not even close to that.
Examples involving engineered things are inherently invalid and don't work. Evolution is like shaking up a solution of many substances and the heavier substances settling to the bottom, the lightest substances floating to the top, liquids separating based on density, etc.
Take something like the evolution of the eye.
I believe you mean a hypothetical evolution of eyes since no one knows how eyes evolved, or if Darwin's theory is even correct.
The key is that it doesn't all just come together in one swoop.
Correct. All acceptable proposals for how eyes might have evolved per Darwin's theory of evolution involve very small changes over long time periods.
Sure there's an element of "chance" and probability to it,
It's better to say that it is simply entirely random. The moment you claim a "probability," you put yourself on the hook to explain both what that probability is and how you computed it.
but there's also a HUGE amount of time to do it in.
Correct ... according to Darwin's theory. If some Christians are correct, everything happened a few thousand years ago, and I'm going to have some explaining to do when I get called into Peter's office.
Evolution has the advantage of working on life over the course of millions of years.
Well, it has the advantage of working over a long but unknown period of time. It could be millions of years. It could be billions of years. Nobody knows.
Small changes add up in that time.
