A few months ago I was searching for something like that too and I tried 3 different mirrors and the VESAUR Professional Lighted Makeup Mirror was the only one that had a a full 10x magnification that filled the whole mirror not like others a small square of a couple inches. It had 3 lights selections and very clear. More on reddit.com

I'm surprised you haven't come across this bad boy as it's the highest recommended in almost every lighted makeup mirror thread. It's insanely good. Been using it for 2 years and it immediately improved my makeup application and is totally reliable. I actually have 1 for home and 1 for my office. More on reddit.com

I just started putting a post it note on the sensor when I use my simple human mirror, keeps the light on. And turn it off every time to save the charge. More on reddit.com

So you propose running NM-B ("Romex") from that box to a new box nearby? That appears to be a GFCI outlet so the black hot and white neutral are (should be) on the "LINE" terminals and there is (should be) nothing currently on the "LOAD" terminals. The hots and neutrals in the red wire nuts are non-GFCI protected which is fine for lighting unless the lightning is in or near a bathtub or shower. Those wire nuts are probably fine with one more conductor. Ideal 452 red wire nuts are good for up to 4 #10s. You'll also need to extend the ground. Remember to leave a minimum of 6 inches of each conductor in the box. I prefer 9 inches. More on reddit.com