I think Flatlander is on to something... getting on the stick is something i associate with pilots too.. the control mechanism is a stick.. i drive stick. ( and have for 30 years--How could that be?) and know expression like 3 on the tree,for 3 forward gears, with the controls mounted on the steering wheel shaft, or 4 (or 5) on the floor for floor controlled shifting, but i don't associate getting on the stick with driving. -- but it also might be related to radios some how.. since nowdays getting on the stick is usually about communicating information.
ps. i learned to drive with 3 on the tree, went on to 4 on the floor, and now drive 5 on the floor.