The moon was pretty bright on Friday night/Saturday morning, so a headlamp wasn't needed for the fire road. It was needed from time to time after the restaurant. Once I hit the backbone though, I used the headlamp most of the time. The trail is really clear of rocks, but it's a bit tough to see the rocks that are sticking out of the trail a few inches or so. So, yes, a headlamp is needed as there are a couple of dangerous spots (everybody knows which spots) and you need to keep an eye on the trail.
As far as which brand......I have a Black Diamond, but I think any good headlamp should do well.
Also, when I do this again, I will be going the Bowl and going past the ski hut. You definitely need a headlamp there. The problem with the backbone is it's really long, but I wasn't sure how well I could see the Bowl Trail, so I chose the longer route.
BTW: It was extremely warm up until near the top. I was sweating up a storm and I only had one light shirt on. I started with two shirts, brought a jacket and an extra shirt, but they ended up being extra weight. BUT, you should always be prepared for extremely cold temps on the top of Baldy. I've been there at noon in the middle of Summer and froze my butt off. Starting temp for this hike was 64 degrees and it didn't get much cooler and there was basically no wind, just a light breeze from time to time.
As a note, there was a barbecue up at the restaurant that coincided with a moonlight hike. At 1:00 in the morning we ran into several people coming down the trail, including two very DRUNK women. They had been up at the barbecue. There are also hiking groups that arrange full moon hikes up Baldy, so you may want to look into them.

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