That whole "enhancing the wearer's existing nature" thing. Maybe that's why hobbits turn invisible with it - they hide from bigger folk a lot. It's their existing nature.
In which case it wouldn't turn Gandalf invisible. It would do something completely different.
I believe that it is noted elsewhere by Tolkien that the Nine and the One both have invisibility powers when worn by mortals. It is suggested by some that the Nine *aren't wearing* their rings during the trilogy, so they aren't invisible. Sauron doesn't have the One to control the Nine, so he's taken those rings personally as a way to control the Ringwraiths.
Note that Gandalf and Saruman are not mortals. And Galadriel isn't really either. They may already exist in the spirit realm, so that the One may not work the same way on them.
Also, the only people we ever see use the rings are stated to be resistant to its effects, and know squat-all about magic. They get to use only what the Ring allows them, and can exert little or no control over the ring, where others might be able to. Maybe more knowledgeable wearers can choose to be invisible, while the hobbits can't turn the things off.
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