For the HP Prodesk G4 (and other HP models) if the Keyboard or Mouse isn't working in the UEFI Firmware or Grub menus the workaround in the JetKVM is to go to:
Hardware -> Settings -> USB Devices
and select Keyboard Only in Classes.
There is something wonky with HP devices USB HID support at Boot that means it won't detect JetKVM USB HID devices if the Classes option is set to more than one item in the Classes list.
Weird