The mirror was useful in lighting the pilot for the deep well burner.  You had to do that with the pan removed so that the gas would rise properly and not blow the pan out of the well.  You also had to kneel or bend deeply from the waist to get the match to the hole. Maybe the light coming down through the well with the pan removed allowed the user to use the mirror to direct the match to the hole for lighting.

Some safety agency determined that gas ranges could not have controls for the burners above the burners.  That was the end of the Globe venture. The neatest one I ever saw had airplane type controls for the burners.  They consisted of a red ball on a chrome shaft. Down was OFF and up was full ON.

As for the controls, there was an oven thermostat and a timer dial on the front of the backsplash and the little damper control. The timer was set according to the Dutch Oven recipe and at the end of the "gas on" time, the timer shut off the burner and caused the oven vent damper to close, shutting off the draft through the oven. Greg can tell you that heating that cast iron plate in the bottom of the oven made preheating take forever, sometimes longer than a short baking operation.