A fog-free shave in my shower since 2013.
ToiletTree’s Fogless Mirrors come in regular, LED, and travel varieties. The LED model happens to be cheaper than the un-lit one at the time of this writing, but as you can probably guess that’s not always the case. Once you’ve started your shower, simply fill the mirror’s reservoir with water to keep fog at bay.
Both of the permanent mirrors include ridiculously useful shelves, and attach to your tile with double-sided tape and adhesive. They also pivot to account for differing user heights. All three mirrors include a squeegee (that actually works!) for cleaning.
The travel mirror, by necessity, uses suction cups, and these probably don’t work, given that no suction cup has ever worked in a shower for longer than five minutes. But then again, none of the other fog-free mirrors worked before these, either.