I would install a flourescent light fixture with at least 2 bulbs bc it's going to be recessed

I'd put something above the mirror always looks nice and bright. Bright makes the room look cleaner.

So your floor guy is going to perform electrical work? Interesting concept to say the least.

Here is my standard bathroom reply below.... regulars are you tired of reading this? LOL !!

Let’s start with the shape of a human head itself. Our heads are tapered downward from our cheekbones. Fixtures that just deliver light from the top of a mirror; only illuminate the top of your head. They produce a distinct shadow below your cheekbones and nose. This creates a less-than ideal reflection of the lower cheek, jaw line and mouth. The image below shows optimal light fixture selection and placement. Compare it to your makeup area. Is there a difference? Talk about “seeing the light.” Enjoy Your Project ~ ClearLED.biz

3 cans and two sconces.