I have learned a bit about gator behavior while diving the Cooper River in Charleston SC. I have dove it about 100 times. Of course there is the exception to everything I am posting below.
One of the first things I learned about gators is that they do not spend much time in the center/bottom of the rivers. There is nothing there for them. They prefer to hang around the edge of the river.
Gators are ambush predators. As a general rule they lay in wait.
Gators are scared of boats and it is hard to get near them.
Gators are most active in the morning sun and at twilight
Gators like tall grass or growth that hides them.
Gators stay in their territory which appears to be about a 50 foot semi circle. I am sure it varies.
If you go into a gators territory, he is likely to come investigate.
Gators like sunning in the afternoon and laying under the edge of the water
If you can, stay away from the edge of a river, especially where it supports tall grass.