Can't get mouse axis input without rmb or lmb down

This question has been going on for a while and it doesn’t seem possible to get axis input from mouse movement in GameAndUI input mode without pressing rmb or lmb. For example, I want to be able to hold down a keyboard key which will hide my mouse cursor and rotate camera around character with mouse input, but am not able to do so. Switching input mode to GameOnly would work, but is not an option for this specific project.
I’ve tried some ridiculous ways to solve this like faking a mouse click with a key press, but as you may imagine this eventually leads to very confusing problems as mouse buttons are used for other things and it won’t differentiate between a “fake” and a real mouse click.
Is there any actually sensible solution to this?