There is a question “If I have tension in my shoulder or hips, I can bring attention them and release them. But, with my neck, the opposite occurs. Bringing attention to my neck causes it to tighten up.”
The following is my answer. How about, not paying attention directly to the neck, but shifting attention a bit to the head? Think that the head is above the cheek bone, where is slightly higher than the neck. You then sometimes had better move your head (turn to right and left) with attention to the head (again not the neck). If you move your head (while torso is still), your neck tension is changed and could be eased potentially. So, when you want to do something with less muscle tension in the neck, you had better think that the head can move anytime (the state that the head is ready to move) and do something with this attention.
I have an idea that we tend to give excess muscle tension if we pay attention to the muscles when we do something. (In this case the neck is where the muscles are located, so paying attention to the neck tends to give excess muscle tension.) We had better pay attention to the ‘edge’, the leading part of the body. (In this case it is the head.)
The neck condition is easily affected by the condition of the lower part (the torso and legs), especially how you support your whole body. You had better pay partial attention to the feet (or the feet and bottom when sitting) and think like your weight on there. You also had better do something with breathing out instead of holding breath. If we hold breath, then it means we tight the abs (and, in turn, neck). Muscles in both the abdomen and neck mostly tense together.
You may think that this is too much to manage. For me it is easy. You probably need to take lessons to integrate these attentions. That is the easiest way to learn this.