Mine does it too. I notice it when I first get in the truck and get my pants and manhood situated.

Take a look at the seat base mechanism. When I looked into what did this, it seemed like all the pin holes in the seat base had a small amount of play. That buildup of tollerance is what causes the rock back and forth. There isn't much that you can do about it unless you want to overhaul the base with tighter tollerances.

 

I just found the seat clunk, play, wiggle, or whatever you want to call it.
The front seat cross tube broke! The tube had torn over time and finally just gave up. Now my seat is like a rocking chair. I will pull it and take a photo. i have a good idea how to fix it too.
Stay tuned.