Q and E switch the AWD/DIFF any time when the wheel is NOT operated such as standing still.
As soon as you operate the wheel and create inputs, the Q and E inputs from the keyboard are ignored. You still see the "flickering" as soon as a key is pressed, but it has no action. See from 25' in the video.
By the way, the current LIVE Version does not have this behaviour. And it does not matter if I use a direct input or logitech legacy. Pressing a wheel button for awd/difflock works, but e.g. assigning to a wheel button a simulated keystroke fails the same as any other keyboard input.