If it’s just precision you’re after, not reach (i.e. you don’t have a problem manipulating your arms to reach the spot), consider setting up 2 mirrors facing each other, at a slight angle. You need the slight angle to avoid your body fully blocking the view to your back.
Stand between the mirrors (or hold one in one hand with your back to the other mirror). This will give allow you to see what you’re doing. As a bonus, by reflecting off 2 mirrors, your left/right will be the image’s left/right respectively.