All the gearboxes I ever worked on had reverse light switches operated by the internal selectors. But from looking at real.oem think you are in luck. The reversing light switch looks to be external and operated by the linkage. Try to forget where the gate tells you reverse should be and just feel for it. If you can hit it, at least you know the box is fine and its just a 'small' matter of the linkage. You might also have a think about the mounts - is it possible one is soft and the box is leaning to one side? If so you might not be able to get the lever over far enough to get reverse