It's awkward to click the mouse wheel. Have a thumb button? Use that instead!

Start by identifying the mouse:

 # lsusb
 Bus 005 Device 005: ID 1532:006e Razer USA, Ltd DeathAdder Essential

Here's the content of /etc/udev/hwdb.d/my-mouse-config.hwdb

 evdev:input:*v1532p006E*
  KEYBOARD_KEY_90004=btn_middle

How did we figure out the '90004'? To be continued...