We drove from Mt Rushmore to Legion Lake during the day via Rt 16A (Iron Mountain Hwy) to Rt 16. You probably won't have any trouble with it at night. An easier route is to turn west on Rt 244 as you leave Mt Rushmore. Take 244 to 87 to 89 and east on Rt 16 at Custer. That's the route I would take at night. I wouldn't recommend taking Rt 87 (Needle's Highway) all the way through the park at night. You won't want to miss it during the day however.

Last summer we drove all around there, and definitely see the Needles Hwy in the daytime if you can. It's really cool! It has these pigtail turns that wind around, and great views of the Black Hills, the cathedral spires.
I have to have maps when I travel, and I remember it was very difficult to find a map of the area, but finally I did. I would google Custer State Park, the Needles Hwy, and you may find it. Sorry I can't remember the exact site where I found it.
We liked seeing the Crazy Horse Memorial and Wind Cave Nat'l Park also.

Devonmcj's route 244 to 87 to 89 still has the switchbacks & tunnel going to Sylvan.

At night I would drive 244 to 385, turn south toward Custer, then east on 16A to Legion.

You are absolutely right LHS. I made a mistake. I hope MBM left before she read my advice.