Help cleaning 16 year old adhesive off rearview mirror

My car had a mirror the previous owner attached over top of the actual rearview mirror and I removed it. Unfortunately was not just held on with the clamps but also really really old stubborn adhesive. I'm a little hesitant to try adhesive removers like Goo Gone since I don't want to damage the mirror and give it those brown marks you see on older car mirrors, not sure if It would do that if it got between like the plastic bezel. I've gotten a good bulk off with my finger nails and window cleaner but that's just not cutting it. Does anyone have any advice?