In the inspector you can clearly see the value of “rot” changing, but it doesn’t seem to be affecting it to the propertie “Rotation” of the skybox material.
Your code is not working because the rotation of a Skybox is a value that must grow. You must think that you are moving an object along the x axes. In both cases the value must grow, but Time.deltaTime don’t do that.
You mas use a global variable that grow with the time… → Time.time