Is there a way to constrain separate axes of rotation and use two constrains as aim and parent ?

I have a character head, that I want to "aim" towards pointer while using x and y rotation axes and rotate character's head sideways while using z axis.

I tried multiple ways of doing it (deselecting repetitive axes of constrains, set driven key, connection editor), non of them worked. The error that I get while trying to constrain not repetitive rotation axis is " Object is already connected."

Any solutions to that, or other ways of doing this ?

I could just parent neck joint to neck controller for rotations, but then I'll lose ability to aim towards pointer...