There is a product called "Quake Hold" that is pretty commonly used in California. It's a soft clay type material that you stick on the bottom of vases, glassware, picture frames, etc. to keep them from falling off shelves, etc. in an earthquake. It holds pretty well and comes off without damaging the piece or the surface it was on. Museums use it also, so you know it won't damage either your mirror or the mantel surface. If you're not located in earthquake country, you can probably find it online. I would think that it would work well to secure your mirror.

I'm not a big fan of mirrors that reflect ceilings. However, if it would fit with your decor, you could age the mirrored surface so that you could get the sparkle without a specific reflection.

The reason that the mirror is reflecting the ceiling is that it is leaning. If a mirror is hung so that the wire is a little bit long, then it will lean out a bit at the top and reflect the room (Or a view out the window) instead of the ceiling. Mirrors also reflect light, which helps brighten a room...I learned that on a school field trip to Williamsburg many years ago...

Love Beverly’s second one ... that kind of antiqued glass is beautiful. And those sizes she’s showing really make a statement. Mirrors don’t just have to reflect something gorgeous on the other side of the room ... they’re art in their own right and are wonderful at reflecting light, adding dimension, and making a room feel bigger. Classic design. This thread made me think of this link I’ve had saved a while: https://curatedinterior.com/parisian-fireplaces-mantel-decor/