Gazing ball- Is there any way to bring back the shine?

Usually the products used on them on inside.You options is to repaint it with a reflective outdoor paint.Heres something similar that was asked on a different forum with no positive answers.https://garden.org/thread/view/15720/New-life-to-old-gazing-ball/

If it is actually stainless steel and not painted glass or painted metal, you can polish it up again with Barkeepers Friend and a scratchless scrubby. It makes stainless steel look like new again. I've used it on my stainless clad cooking ware that I bought in 1969 and it still looks like new.

Try using a clean rag with 91% isopropyl alcohol on it. I clean my stainless sink with it and it just shines.

If it doesn't shine up with polishing you can get mirror finish spray paint to give it a fresh finish.