I wish they made a diamond bit for the roto-zip. Thier bits for tile burn real quick on certain types of tile, and are useless on stone. (Turns red, and its toast) Grinder works on all, and Roto-zip realized this and made convertable models Grinder/router. They make a smaller 3"? diamond grinder wheel special for it, but its really hard to find.
Back before the roto-zip, I would lay out an outline of the box. And use a 1/8 masonary bit, drill holes real close together, pray, and crack what was left between the holes.
And heres some personal experiance advise.... If at all possible, physically or visually check that there are no obstructions in the wall. Back when I did alot of this, I would refuse to do it (Cut tile or stone) unless I could cut a hole for a dental mirror above it, or the other side of the wall. That hole is an easy patch, compared to finding that there is a stud, backer, drain/vent. I think that "Stud-finders" in situations like this are un-reliable through metal or wood lathe, or tiles. Theres nothing like cutting the perfect hole for your box, then finding that the counter and splash were backed by a 2X that you now need to chisle out, that a stud sensor didn't see. (I treat base boards the same way)
