Yes... so, what you are seeing is breaks in the chrome where the undercoating of copper is exposed and corroding, hence the green... like a penny. Evaporust will knock it back, but you'll be left with some rough chrome. I don't know what your goal is, so share that. Either way... that black "deck" sticker... peel that off before you soak it in anything. You can clean that up separately and glue it back on when you're done.
Based on that, my recommendation is pull the entire thing apart (Keep pictures of the order in which you pulled out all the washers... and share those pics with me! ) and soak in Evaporust. You can machine polish the internals, but I would hand polish the cover with a cleaner wax.
That "glass" can be removed gently (it's glued) and you can wet-sand it with 2,000 grit, then hand polish with the cleaner wax.
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