Until Dawn : What was the light on Sam's head towards the middle to the end

Was it a headband that lights up

It's a flashlight that you don't need to hold in your hand. I'm not familiar with the gear but I imagine it's purpose is for climbing, since the rest of her attire seemed to support that as well.

I think it was really Beth's watch that lit up because Sam found it in an earlier scene and she just wrapped it around her head.

Although I can't figure out how a girl's watch can fit around her head

Didn't she have the light on when she found the watch?

It's just a headlamp, they are very common in real life but maybe less used in movies.