So, right now, it appears that the Elantech 1203 touchpad is not supported due to a kernel bug. As it stands for me, nothing pops up in dmesg, xinput, or libinput about it, but if you look at the /sys directory you can find /sys/bus/i2c/devices/i2c-ELAN1203:00/
Also, I have found this kernel bug that shows a recent patch, but as far as I can tell it hasn't been accepted into mainline yet.
https://bugzilla.kernel.org/show_bug.cgi?id=213579#c56Everything else for the laptop works right out of the box, so sucks that this currently doesn't.