An image of “the head up”
If we pull a rope (right in the above diagram), the top of a pole moves up in rotation. Our head moves up like this kind of scheme.
“Up” is generated by mainly the muscles in the back, working together with the muscles in front. The head actually moves up a little bit rotating counterclockwise in sagittal plane (when a person faces to left like diagram). There are some more muscles involved in this movement, though. By the way, our movement are mostly rotation.
Just intend “the head up”
We don’t have to intend “move the head up in rotation”, or we don’t have to try to use the back muscles or the longus-capitis to move the head up. We just intend to move the head up (probably better with “against the bottom of the feet”), and the head will move as this with recruiting adequate muscles and minimum contraction. This is following “original objective intention”, my hypothesis.
What pulls the head back and down?
It’s not the sub-occipitals to pull the head back and down, but the sternocleidomastoids. The sub-occipitals are too small and short to generate that kind of moment. Since the sternocleidomastoids are attached to the relatively rear part of the skull, its contraction leads the head backward rotation and downward (and a bit forward). So, to support the head against the pull of the sternocleidomastoids we have the longus-capitis with the help of the front side neck muscles. They locates at the front side of the cervical spine.
More detail is in my past post here:
By the way, the sub-occipital muscles are more for stability and fine tuning of vision, hearing, and smelling according to the text book, “Kinesiology of the musculoskeletal system”.