Well, it's true that the "gear shifter" goes in the middle, and depending on wether you drive on the left or the right side will indeed decide on which side of the stick you will be sitting. However, the reason for driving on the left side can be traced back to the old sword-smacking-days. You would normally pass oncoming riders on the left so that you could either hail them or strike them down with your favourite right hand, so indirectly, gear shifters ARE handedness.
I heard somewhere that the reason why some countries switched to the right side had to do with their king being left-handed, but I can't (or won't, pick one) verify that.