My guess would be that there is some start-up sequence that should happen automatically when the ignition is turned on. That start-up sequence stops working due to age, and then you manually perform the start-up sequence with the fuse.
It's possible that there is an electrolytic capacitor that is too old that affects the start-up timing, that could be replaced.
Also there is no end of different issues that can be caused by poor battery states and poor connections. I wouldn't be surprised if the problem is a symptom of a weak battery or a bad connection somewhere.
There are lots of guesses in what I've just written. l would try to find a circuit diagram of the display unit before going any further. Also if it's as common a problem as the video suggests, there may be a fix if you search for it.