I spent the night on top of Baboquivari with the University of Arizona Ramblers hiking club years ago. We had a fire from remains of the ancient lookout cabin of the 1920s. The next morning a group of us had to go all the way to the end of Lions Ledge.
Slightly more iconic for me was climbing Weaver's Needle and spending the the night on the top there. We climbed up the final couple pitches with flashlights in our mouths. This was long ago. I did have a headlamp but it was Giant and bulky and I only typically used it for caving. I recall my buddy saying - don't move more than two feet to your right because it is a sheer cliff. There was no moonlight. The next morning I stood on that same spot with a whole lot more trepidation because I could see the exposure.