Thanks Palimpsest for your explanation, sorry to take so long to get back to reply. Your first two paragraphs make sense, and others (builder, bathstore personnel) have agreed it's not a good idea to drill other things into the mirror. We were going to try to choose an alternate lighting fixture for this guest bathroom, but they had already glued the backplate on to the mirror, so we'll live with this one. But at a later date, if we ever did want to change, will that be "impossible" without risking breaking the mirror to remove the backplate? By your last paragraph, do you mean that if we put up a train rack (or whatever... say smaller towel rack or toiletry holder) that required drilling, that we just have to know where the pipes/whatnot are behind the wall before accidentally drilling into them? These tiles, being "very hard", apparently went through a lot of drill bits for whatever they did need to drill for. And presumably a train/towel rack should be mounted to stud underneath too, for extra stability? Actually, at some point I think we'll want to have a grab bar installed... so same points would apply, with extra of figuring out best angle/height to suit most users (being guest bathroom with potentially some heavier and/or older visitors) and ideally also esthetics. Eventually we'll aim to have grab bar(s) for master ensuite too, so whatever we learn will be useful there too.

debdiy - do you have a tile backsplash? If not, you could do one like herbflavor describes. If you do have tile, you may be hesitant to drill holes in it, but you could. As for drilling into the underside of the cabinet, that's iffy. You'd be drilling into the layers of plywood from the end or into the end of the mdf/furniture board. Neither of these is strong and is not likely to hold. If you search on Amazon for "pot racks" you get 1802 results. Maybe something in there will work for you.

We needed more hardware than came with the shelf :) We purchased bolts long enough to go through the shelf and then through the "slit" of the pot rack where the hooks go. We used a washer to prevent the nut from falling back through the slit. Then we drilled holes aprox. 3" in from the edges along the long center of the shelf and bolted the pot rack to the shelf. We can adjust the height of the pot rack by adjusting the shelf height. Right now the bolts hold the pot rack so tightly to the shelf that the hooks cannot move. I need to loosen the bolts a wee bit and adjust the hooks better and then retighten them. In the picture below you can see the bolt between the first and second hook from the left.

The most gorgeous one I know is by Howard Kaplan, called the Europa Arrow Pot Rack. Very french-professional-kitchen looking. Also, check Sur La Table, they have less expensive bar pot racks by J.K. Adams. Sur La Table also has the Enclume "bookshelf racks". And as Gsciencechick mentioned, Williams-Somoma has a couple Enclume wall pot racks. Or go to enclume.com for the Enclume entire line. Here is a link that might be useful: Howard Kaplan Pot Racks