Ok, this morning I got tired of that squeaky noise problem and wasting my time with the dealership so I decided to tackle the problem myself.
I backed the Chevelle up out of her sleep in the heated garage and into the cold. Followed the proper procedure to remove the seat from the truck and began inspection.
I found that the foam of the bottom seat was un-protected at one place and was touching a plastic part in a way that, when moved, created the exact same sound than in the truck. You can ear that in the video :
https://www.youtube.com/watch?v=4TKdpPj1uAY
Semi-temporary repair was to isolate that whole area with a piece of cotton rag that I had on hand. I did both sides juste to make sure.
Now the truck is back in the cold, and I'm waiting for tomorrow morning to see if that solved the issue.