I know it sounds outrageous but the recommended method is with small pads o f blue tack. A glaziers will sell you these or your local stationers. I use d this method 20 years ago to fix a 1500 x 500 mirror on to a cupboard door and it hasn't budged in all that time. They hold the mirror close to the vertical surface so all the weight is onl y transmitted downwards. As you will find out if you try, it is relatively easy to hold a mirror against a wall using light pressure only. Much easier than just holding it by its bottom edge.
Bring on the doubters and nay sayers.
Experience speaks louder than words.