+Spell Level from wand not applying to Skill Gems

I am seeing the + spell level from y amulet on the skill gems, but not from my focus nor my wand. It only shows the +2 global modifier. I have tried checking in combat when I am using the weapons and thus they should be equipped, but it is not showing there either, which makes me wonder if it is being applied?

I figured it out. If you do not have anything in your second weapon set, it will not show the skill gems and you do not show using the wand and focus when casting. When you apply the 1st weapon set to the skills and disable the second weapon set for them, then the +spell levels applies.