is the mirror round or oval?

or is it square or rectangle?

With the square or rectangle, you could easily place a white frame around the mirror with a bit of custom css code, with the mirror having black background, this white frame might just be enough light to not have to worry about external light reflections.

Add this to the top of your custom.css file:

html {
  cursor: none;
  overflow: hidden;
  background: #fff;
}

body {
  margin: 60px;
  height: calc(100% - 120px);
  width: calc(100% - 120px);
}

then adjust the size of the frame to suit the needs:

note that the height and width are 100% -
So, if you change the margin size to 80px, you’ll need tot change the height & width to 100% - 160px

Play with those numbers and see if you can get a good lighting with the mirror’s built-in frame.

My example:

with margin: 80px and H & W at 100% - 160px

I’ve made several vanity mirrors but I never used lights. However, I will voice my opinion:

As long as the lights are not in front of the acrylic, and not shining on the acrylic, you should be alright. Lights shining on the acrylic, not so good. Lights shining on the person in front of the mirror, very good.