Touchpad not working on Debian 9

# egrep -i 'syna|alps|etps|elan' /proc/bus/input/devices
N: Name="SYNA3388:00 06CB:8459 Touchpad"
P: Phys=i2c-SYNA3388:00
S: Sysfs=/devices/pci0000:00/0000:00:17.0/i2c_designware.0/i2c-4/i2c-SYNA3388:00/0018:06CB:8459.0001/input/input17

Your touchpad is not connected to the system via internal PS/2 or USB wiring, but using the I2C bus. This is a fairly new development, and Debian 9's standard kernel might be too old to support such touchpads very well. You might try with a backport kernel.

See here for instructions in enabling the Debian Backports repository - basically, add this line to the /etc/apt/sources.list file:

deb http://deb.debian.org/debian stretch-backports main

Then you should be able to install a backport kernel with:

apt-get update
apt-get -t stretch-backports install linux-image-4.19.0-0.bpo.2-amd64 linux-image-amd64

After a reboot, you might then have better luck with your touchpad.