The diagonal mirror was orignially a feature of Gerstner wooden toolboxes. The reason for the mirror given by the Gerstner Company here is:
The mirror was first installed in the early 1900’s on some of the very earliest Gerstner chest designs. In those days, very few manufacturing and/or tool & die companies had indoor plumbing. In other words, there were few companies with lavatories (with wash basins and mirrors) for toolmakers and other factory workers to use to clean up at the end of the day.
The “mirror” mounted inside a Gerstner tool chest provided the wherewithal for the chest owner to check his appearance and comb his hair before heading home (or, perhaps, going in to ask the boss for a raise). At various times over the years, we have introduced a few tool chests without including a mirror. Interestingly enough, the feedback from customers has been, “Without a mirror, the chest doesn’t look like a Gerstner.” So . . .you may notice that virtually all new model Gerstners feature a“mirror” inside the tip lid.
They don't mention why the mirror was placed diagonally, but I recall reading somewhere that it was more as a trademark feature of the Gerstner brand rather than for any practical purposes, a feature now copied by other manufactures, particularly those in the Far East.