I also recommend not using glass, especially since the "shiny" on the back of the mirror will probably flake a bunch around your holes, but drilling glass, even large holes is no big deal. All it takes is time. I have personally seen 10 inch holes cut in half inch plate glass with no special tools, other than a drill press.
For smaller holes a normal carbide masonry bit works fine. You make a ring of plumbers putty on you glass around the hole, and pour some kerosene init, so you are actually drilling in puddle of kerosene. Run the drill slowly, and use light pressure, and make sure the glass is well supported underneath. The kerosene accelerates the crack propagation as the glass fractures off.
For bigger holes you need to construct a hole saw. My dad did his 10 inch holes (actually he was making 10 inch disks) with a circle cut out of plywood, around which he nailed a strip of sheet metal, and which he attached to a small faceplate, basically a flat metal circle with an axle attached so he could put it in the drill press. Then you put a little water and some abrasive powder on the glass, and once again using a slow drill speed, but this time more pressure because it is a ring not a point you are pressing on, just take your time, adding just enough water to hold the abrasive where it belongs, and adding a little abrasive now and then. Al that fancy diamond bit stuff is only needed if you intnd to do it on a regular basis, and your tools need to last. If you only need to put a dozen or so holes in a control panel it's a lot cheaper to make do.
kamakazi