I have to admit I didn’t read it all in detail. The key information seems to be that the touchpad is supported since kernel 4.14 and that secure boot must be disabled.
It’s not a problem of the touchpad no working, it works and is always on.
There’s no function key to enable/disable it, at least not in the user manual.
Also, the touchpad light is always off. The on/off button (a depressed spot in the top left corner) doesn’t work.
IINM it worked in windows 8, but I’ve nuked it - and good riddance, it was slow as molasses.
The ID is for the example a responder used in the thread, not related to the problematic touchpad. (Yay Google translator)
Kernel version is 5.3.18, so more recent.
Secureboot is disabled. Actually, it is grayed out, can’t be enabled, even with legacy mode (CSM) disabled. Weird, but this is a topic for another thread, maybe.
Aaach, blast! I was too optimistic after having found the ID and didn’t read it all in detail. Unfortunately, other search results to this ID are rather less helpful. I might ask if xf86-input-synaptics is installed? But since your issue isn’t operating the touchpad but the on/off button - LED it seems to go deeper. :\
Hmmm. That actually says “Not supported in Linux Ubunto”, not really that is not supported in Linux. Who knows?
… but, it would be kinda nice to know what Desktop you are using. In XFCE, you can go to Settings, Mouse & Touchpad, select the Touchpad and turn off the onscreen button.