16.04: Elantech touchpad not working on new laptop

I would suggest trying the libinput driver. It's much newer than evdev and synaptics and fixed some issues I had with the Elan touchpad on the computer I use. It also supports most of the hardware of other drivers supported, including some graphics tablets. Instructions:

  1. Install the package xserver-xorg-input-libinput

    sudo apt install xserver-xorg-input-libinput
    
  2. Uninstall xserver-xorg-input-evdev

    sudo apt remove xserver-xorg-input-evdev
    
  3. Uninstall xserver-xorg-input-synaptics

    sudo apt remove xserver-xorg-input-synaptics
    
  4. Reboot and see if things work better.