I'd prefer not to touch the mirror surface (even at the edges; with paper or otherwise). Here is how I did it:
I laid the mirror on a flat surface; Placed blocks of wood around it that are just a little thicker than the mirror, so that I could lay two metal rulers at right angles over the top of it without the rulers touching each other or the mirror. Then I carefully looked directly down at the centre mirror and using the mm markings on the two rulers I visually figured out where the centre is and marked it with a fine tipped permanent marker. Then I stuck a triangle shaped marker around the spot. I cut it out of dark blue strong cloth-reinforced tape. It stays on no probs when I wash the mirror.
If you have dandruff, get a good anti-dandruff shampoo and use it before attempting this.