@kjleitch Hi and welcome to the forum.
Gnome tweaks is available in Software for Core users.
There is a useful Mouse/Trackpad test screen accessible from the settings page. I have edited OP’s screenshot to highlight that button. (I recently found that useful whilst diagnosing a sick mouse).
[mouse]
(sorry that screenshot not english language)
You could also look at these threads to see if anything helps:
Hi, I could turn off my touchpad by pressing F6, and then the touchpad turns off. However, on startup, the touchpad is set to on automatically. I again have to press F6 to turn off my touchpad. I don’t want to disable it entirely. I just want to turn the touchpad on when necessary just by pressing F6 again. What do I do?
BTW, mine is a Lenovo Z50-70 laptop.
You may need to check whether your touchpad uses elan or synaptics.
There is a current bug report on this issue.
It appears that your steps are correct. You did everything right. The repo and the package appear good.
However, there may be one additional step needed:
Please try applying this patched kernel (Install the .deb package) then reboot and boot into it. Let us know what happens…