Just a quick note on how to get the Logitech M720 detected and paired under Debian Stretch.
According to Logitech specs, this mouse uses „smart bluetooth“, meaning it’s a low enery device.
As the mouse was not detected via blueman graphical interface, some steps were neccessary to get the mouse discovered.

First make sure your bluetooth adapter is running properly.
Then install blueman package via apt.

open a shell and start a LE-device scan:
sudo hcitool lescan

this will get the mouse detected in the following scan:

open a second shell and run:
bluetoothctl
scan on
pair XX:XX:XX:XX:XX:XX
connect XX:XX:XX:XX:XX:XX
trust XX:XX:XX:XX:XX:XX

done.