From what I could tell from the video. The guy just adjusted the shift rod, gear selector, and the indicator light to be lit for whatever gear the transmission was actually it. And not adjusting the actual transmission for the shifter. If that makes any sense.
In other words he had the transmission shifted into high, then moved the shifter itself into high before loosening the shift rod to adjust the high lamp indicator to be lit. In doing so, he may have actually changed the position of the transmission into low or neutral. If so, the transmission could have been in low, for example and the shifter and indicator light could have indicated high. Make sense?
I'd still remove the shift rod, then make sure the transmission shift easily into low, high, neutral, and reverse. You may need to rock the machine forward and/or backward just a little. And make sure there is not a lot of slop/slack in between the positions. Then move the transmission into reverse (or low), then move the gear shift handle into reverse (or low), then eyeball and adjust the shift rod to fit into the location. Then adjust the rod length to make sure the correct directional indicator lamp is lit. Then move the selector into the other positions and adjust the rod as needed.
I haven't looked at mine and the diagram doesn't say. But I'd bet the shift indicator selector switch is located somewhere near the shift selector handle. Does any of this makes sense?
I'm not a mechanic, so take the advice as someone that is just trying to help. Remember listen to me at your own risk.
Good luck and let us know how it goes.