I think a big stick (make that a rubber hose since it will not leave a mark) will solve the trainers obsession with right hand left hand.
Here is what you do, when he takes his left hand off the wally **** hit it as you should never drive a forklift with no hands on the steering wheel.
When he removes his right hand from the wally **** hit it as you should never drive a forklift with no hands.
when your trainer smartens up and decides to do the switch with both hands on the wally **** go ahead and give both his hands a smack as it is not safe to drive a forklift with two hands on that little silver free wheeling wally **** at the same time.

Legal disclaimer -- NO TRAINERS WERE INJURED DURING THIS PRACTICAL TRAINING SCENARIO as this was only a tongue in cheek response to an ill thought out idiosinkracy of a person being paid to train lift truck operators.