I don't notice any movement on accel/decel, but turning right makes the gas gauge go down, and turning left makes the gas gauge go up.
I had a Cadillac that did the same thing... so has every vehicle I've ever owned.
No matter what, my CiViC gas gauge always measures lower at startup, then when I'm moving - sooo... I think it just makes an educated guess, so to speak, e.g. averages it out.
Basically, I go by the odometer - and to hell with the gas gauge!