That you state this happens when you are trying to relax tells me this is more of a tension problem than anxiety. But it can become be a vicious cirlcle. You try to relax, your head feels like it's having a spasm and your eyes feel "jumpy.........." so you feel some anxiety which only increases the tension, which then keeps the anxiety going and on and on it goes.
Spasams in the back of your head are probably just the muscles trying to relax after having been wound tighter than a drum all day. Brain tumors and brain cancer will not cause your muscles to twitch. You would be in terrible pain if either of these conditions were present.
Your "jumpy" eyes are probably a part of this entire system of head and neck muscles............it's all connected!
I could suggest some tension relieving exercises or you can look them up on the NET. The EXERCISES..............NOT SYMPTOMS!!!!!!!!!!!!!!!
Heat packs applied to your neck and eyes, massage, gentle neck rolls, certain Yoga positions.........any, all of these might help.
Try these for a few nights and see if they help. If not, a visit to your doc is in order to rule any injury that may be causing these problems.
And yes, many of us with anxiety issues have these problems as well.
Peace
Greenlydia