Remove touchpad two-finger right-click

I came across https://askubuntu.com/questions/999631/ubuntu-17-10-disable-touchpad-bottom-right-corner-right-click

That pointed me in the right direction.

Running

gsettings list-recursively org.gnome.desktop.peripherals.touchpad

lists all touchpad settings. I'm only interested in

gsettings get org.gnome.desktop.peripherals.touchpad click-method

which at the moment returns fingers.

Now I just needed to know what are the valid options I can set this key to. After some digging, I found range

gsettings range org.gnome.desktop.peripherals.touchpad click-method

which returns

enum
'default'
'none'
'areas'
'fingers'

Finally, running this solved it:

gsettings set org.gnome.desktop.peripherals.touchpad click-method areas

This can be done in the GUI as well, if you like (at least, it can as of Ubuntu 19.04). Use the Ubuntu Software app to install the "GNOME Tweaks" app. Then launch GNOME Tweaks and in the "Keyboard and Mouse" section, click your desired setting under "Mouse Click Emulation". In this case, the asker wants the "Area" option, but you can also choose "Fingers" if you prefer the two-finger right click.

The GNOME Tweaks app edits the same setting mentioned in the accepted answer, it just lets you do it without the command line if you're more comfortable using a GUI.