I watched the videos. It is easy to say that the first video may very well be due to improper installation, or signal interference. Impossible to know exactly. You can't even know what bike these are from those video clips.
I would wire the device up exactly as the Instructions say, without wiring it permanently and test it. If you encounter an oscillating needle, then you have a likely solution (signal filter). But as I said earlier, typically a proper splice into the coil trigger wire (yellow from the ignition point/plate) works perfectly well.
I have seen where folks use a gauge that the sensing wire wraps around the spark plug wire, and have had uneven readings. This is often attributed to surface grime and debris on the lead. But these will work, and they should be very accurate and stable while operating.
Ignore the full sweep at key ON, thats appropriate. Also, when you kill the engine, the needle may hold where it was last until you key ON/OFF. Again, this is normal and not a symptom of faulty function.