No need to worry about light at night. As long as your skink has enough hides that he feels secure in, he will not be agitated that it's dark. Imagine in the wild; there are plenty of nights when the moon is covered by clouds and it's pitch black, with lots of nocturnal creatures out sniffing around.... He'll be just fine in your bedroom
As far as nighttime heating goes.
I've worked out temps so that I have a Ceramic heat lamp and a basking lamp on during the day that makes my terrarium the right temperature on both sides of the tank, and the basking spot. During the night, only the ceramic stays on (which, of course, doesn't put out any light), so that my skinks still have a warmer spot to go to if needed, but the rest of the tank cools down to give a nighttime variation.
But as iLoveMyLizard pointed out, if your house stays warm enough throughout the year during the night, you really don't NEED a heat source for your BTS during the night. This is just what makes ME most comfortable and worry-free

And, oh by the way, this IS the best forum out there!
Edit: I do want to point out though, that 65 degrees at night might be a bit too cold for some species. For example, if you get an Indonesian species, you really don't want to dip below 70. But you can make those adjustments when you know what you'll be getting.
Cudos by the way for getting things figured out, and hopefully set up, BEFORE you get an animal!

Breeder and keeper of Meraukes from 2010 to 2022.