Thank you.
I watched the video on a bigger screen - I can see it now. I think you are driving too fast
I am not a mechanic, I was just working with sender\gauge set in my car. Two things come to my mind:
1. Indeed, some lose connections: at sender, tail harness connector, under dash, instrument cluster. I would start with wiggling those easily accessible while watching the gauge.
2. Gauge itself. What I noticed with gauge bought in internet store - you had to work with the screws that were holding the gauge together, loosen some and tighten some. Then the hand was working properly. There was originally too much tension there that was blocking the hands movements. Also: in aftermarket gauge the fit of the orifice for the bulb was so so. I had o use Dremel to enlarge so that the frame does not push on the bulb (hand was moving, reserve light was coming on as bulb's base was shortening everything to ground). Do you recall any issues like this while installing the gauge? Do you drive with your lights on? Is it possible that something expands a bit because of heat and pushes on something?
But these are just suppositions...