This is the geabox I use in the car. The video shows how the shifter works. The shifter is mounted in the middle of the car, and can be rotated around two axis. The last two photos show how it is connected to the rest of the car. A 3L axle, with a 1/2 bush on the end, is connected to the bottom of the shifter. This axle pushes the black pieces forwards/ backwards. These pieces are connected to the red gear selectors. The two LBG pins make sure the gearbox is in neutral when switching from 1st or 2nd to 3rd or 4th, to avoid jams. The first two photos show the gearbox. It is a very simple and compact gearbox. The difference in ratio between each gear is 1.67.
Colored axles: Light purple: input from rear wheels Orange: slower axle, connected to 3rd and 4th Red: faster axle, connected to 1st and 2nd Green: output Yellow: 1st Light Blue: 2nd Purple: 3rd Dark Blue: 4th