If the mounting hardware would hit a cable, you need only move the mirror a few inches to avoid it.
Cut a small hole in the drywall / plaster and look in the wall. See where the cables go and hang the mirror in a way that doesn't hurt them. Cut the hole in a place that the mirror will cover, and you don't need to worry about doing a good repair job on it.
So, I went with the mastic.
Bad news - between not boing thick enough, and the fact it's pressboard, I didn't feel confident using any kind of screws to hold the door. I went with a pure mastic solutions.
Good news - this in fact a door, so you can take it off. This lets you keep it horizontal, and put weight on it to help the glue hold.
So, I took the door off the hinges and laid it flat. I marked off the perimeter of where I wanted the mirror with blue tape (Blue Painters tape is one of my favorite tools). I thought the surface was a bit plasticky still, so I scuffed it up some with some sandpaper. I put the mastic on the mirror, trying to keep the inch from the edge. By the time I was done with my pattern, I was almost done with the mastic tube, so I just emptied it. I put some 2x4s and other heavy things on top to help the glue hold (another advantage of having a mirror it on a door). I let it sit for the recommended 48 hr set period and put the mirror on.
The only downside I see so far, is the weight on the door. It seems stable, but the wardrobe didn't seem 100% level. What was OK before, what closed fine before, now stays open a bit with the extra weight. My next subproject is re-leveling the wardrobe.
Best Answer
For a "floating" appearance you could use construction adhesive (or "mirror adhesive") to mount a board to the back of the mirror (just the central mirrored part), and use some form of hanger or French cleat to attach that to the wall, with the mirror itself out a bit from the wall.
That would lend itself to wrapping that board with flexible light strip or rope lights to "halo" the mirror a bit and emphasize the stained glass edges by lighting behind them.