Rotate my torso in vertical axis towards crosshair (target)

Hello, folks! While making my Character controller I've run into a problem. I have target object right behing my character (it's assigned to the camera) and all I want is to make my torso look at this object. So, thats all, but it also contain the next problem: when I use a riffle, f.e. , my torso rotated to right and I need to hold it in this position, but also to move it vertically to the target. Which I don't need, when I use a gun, so I need some universal logic which doesn't depend on my current rotation. I've tried to use LookAt funciton but it works not the way I want...

As far as I concerned, Animator.SetLookAtPosition works with the head and Animator.SetIKRotation - with hands and legs. What can I do to achieve result for torso? Maybe other IK logic or smth...?