Ubuntu 20.04, Asus TP300LD. Focaltech touchpad, Xiaomi wireless mouse.

If during boot time the mouse receiver is plugged in then the touchpad behaves weirdly: left button does not work at all, taps do not work.
If I do a stop/start for the psmouse module - everything starts working fine immediately.
If the mouse receiver is plugged in after startup - everything also works fine, no issues.

Any idea how fix it for good?

I've tried enabling the rc.local service and including the psmouse restart in rc.local - it did not help for some reason.