I'm assumimg the switch controls a plug for the lamp???? You can plug the lamp into a smart plug before it is inserted into the electrical outlet. Then the app on your phone can control turning the lamp on and off.

Thank you for your suggestions.

is there a spacer bracket that i can use that will secure the mirror, but leave a space between the wall and mirror?

We have almost all our lighting controlled by Alexa so as mentioned do the same It would be helpful to see your space since IMO mirrors behind lamps have a kind of glam look and the headbord ? Isee is not glam

Have the electrician move the switch. Hiding a light switch behind a mirror is a good way to get the mirror covered with fingerprints.

Why do you want a mirror behind the lamp? While this is sometimes seen on design sites it never struck me as a good idea. It looks odd to me. Of course an electrician could move the switch.

Waiting for feed back I do not think you need an electrician at all just a smart plug

Can you just hang it higher?

If your mirror has a frame, it's likely there is space behind it to accommodate the electrical switch. They are not that thick.