I did not say attach the camera to the eyes as indeed that would be annoying. Instead just put it at eye level with a simple vertical offset to where it is now. The camera is stable enough at my chest level even though in third person views I am doing overexaggerated animations, so the camera is already not attached to the actual body bobbing around. There is no avatar in first person mode so you do not need to worry about the face clipping the camera.
First person view is nothing but animated weapons/tools, there is no body, same way that Skyrim does it putting the camera at eye height. I do not use first person view mods that attach cameras to the eyes of third person avatar, because indeed it is a head bobbing mess. That is not what I am asking for, at eye level is not the same as being attached to the eye. Instead it is simply a vertical offset from the ground where the avatars eyes are in default T-pose.