The Age of Enlightenment and Enlightenment Movement are actually the same thing. Basically, one refers to the movement, the other refers to the Age it occurred.
Part of your issue might be that you're expecting things in the wrong spots a bit. The Civil War occurred in the 1860s, long after the Enlightenment was pretty much "over." The Bill of Rights and Articles of Confederation are certainly in the right era, but towards the end, I'd suggest. Really what you're looking at is the late 17th century until...ohhh, I'd say the Enlightenment really ended with Romanticism in the early 19th century or so. It's really hard to tell, since a lot of Enlightenment ideas proliferated and moved into different sections, like Positivism, Science, etc.
If you're wanting to know more about the Movement itself, some of the people you're going to want to read about include Thomas Jefferson (a choice you probably already know), Voltaire, Kant (who defines Enlightenment, actually), Newton, etc. etc. A lot of this is going to occur before (sometimes far before) the American Revolution. This is because these ideas influenced the Revolution but didn't come from them. So...have at it, young scholar!
Enlightenment Reader ; Extensive reading on the subject.