A lot of spouts are connected by a nipple (short threaded pipe) with female threads built into the spout and male threads screwing into the elbow 90 degree fitting in the wall and this spout. Now a lot of so called plumbers out there no longer can read a ruler and certain manufacturers have resorted to a push on type of spout connection.
FORGET the mirror dude unless your opening a beauty parlor or working on AC systems. I would strongly suggest you try to unscrew the spout
IF you have a spout with a built in diverter OR call a LMP to just replace your shower body with an anti scald type (pressure / temperature)
Then you have a choice of an integral diverter (part of the showerbody) OR a tub spout type again.
Think of it your paying for the knowledge and if you watch the Licensed plumber the next time YOU can be the hero and know exactly what to do. Good Luck