The mirror allows the reamer to be sighted from the top and front at the same time.
I have had numerous requests to post a picture of this device, so I've finally got it.
Years ago I was tasked with finding a way to streamline the installation of 100's of sets of pegs in instruments with very small pilot holes. Collaborating with a colleague we found a few methods of speeding up the process. Although I no longer have large batches of pegs to install I still use the mirror for installing pegs in cellos or on instruments with a twisted pegbox and scroll. With a twist it can be hard to see the centerline, so being able to sight from the top and front at the same time speeds up the process. It also makes it easier to get a really nice straight set of pegs.
In the end I clamped cellos in to this jig for fitting, and used a reamer in a drill on the slowest setting, and probably didn't cut much faster than you would by hand. The real savings was in wear and tear on my hands and the fact that I didn't have to stop and check the peg angle from the front and top every couple turns. I could just keep advancing while siting both angles from the same position using the mirror. Peg installations took 1/3 the time that they did without the jig, and quality was at least as good if not better. I didn't always use the jig for violins, since those installations are much quicker anyways.
If a scroll has a centerline that is hard to sight I will put a centerline on the mirror with grease pencil, and sometimes a couple of perpendicular lines to reduce the time I spend deciding about the angle of the cut. For cellos there is also a benefit to having the instrument clamped in place since you don't have to turn it to see both angles. I also like using stop collars made to set the distance from pegbox to peg collar. I turn pegs to the size I prefer, then sand and oil them. If I back ream the last few turns up to the collar the pegs will be consistent. If you prefer tapered distance to the peg collar (Ex: A peg further out than G peg), then you would set the collar to the longest distance and adjust the las 0.5 mm individually.
As a side note, I have also taken to using a 3x magnifying mirror when carving a scroll. I will place the mirror behind the scroll while it is clamped in a 360 degree swivel vice. When properly placed I can see both sides of the scroll at the same size while carving. Not totally necessary, but it's a nice reference.