If it helps, I have a similar issue with my USB wireless mouse. it works most of the time, but occasionally, it will not work at login at all, so I need to unplug it and plug it back again.
Since both the mouse and (in your case) the touch pad are pointing devices and the issue happens sporadically on login in both cases, I’m thinking it could be the same problem. I wasn’t able to identify the reason, but given that I was able to use the unplugging/re-plugging workaround I didn’t bother too much with it. I suspect the device is not properly initialized for some reason.
Bottom line, if you cant solve the issue, try identifying the device and resetting it with modprobe (which should be the equivalent of unplugging and plugging the touchpad back in):
- first identify the driver by using
inxi -J --no-host - then use
modprobe -r [drivername]followed bymodprobe [drivername]
Without being a proper fix this might help get the touchpad back in working order when it doesn’t work at login.