I use the Alexa cloud function in homeassistant to control mine. I created switches that are tied to command line calls which use the remote module to control the mirror. The homeassistant switches are discovered by alexa as smart home devices. Then you can create routines to do whatever you want as long as the remote module allows it and you create a script to call that function. I use mine to turn the monitor on at night when my sons blood sugar goes out of a desired range. I use homeassistant to grab the BG info and post it as a sensor. My mirror uses the MMM-HASS module to display the BG reading. When I address the issue I can say a command and a light and my mirror monitor turn off.
I can elaborate if you are interested, its not that simply and does require homeassistant running on a home server and i use the paid alexa homeassistant integration service (I believe there is a google home service as well). There is a way free way to do it, but honestly the paid service is cheap and allows you to do so much.