A lot of the time when hiking at night, SAR situation or not, I prefer to hold the light in my hand, generally at waist level or perhaps below,in order to see the ground relief, whether or not I am looking actively for footprints. I will shift the light to my head or helmet when I need to use my hands - actively climbing, rendering first aid,or whatever.

Occasionally I have walked on a trail with the light on my head, losing all shadow relief and becoming quite disoriented. This happens quite noticeably on wide, smooth trails - like the Bright Angel Trail at Grand Canyon. I had absolutely no sense of where the ground was. Once I had the light at a lower angle, everything was better.

I did this a lot when using a carbide lamp, and a secondary benefit was nice warm hands. I imagine this might be true also with some of the more powerful LED lamps.

I routinely carried at least two additional lights (old caver's rule - three independent light sources) - and there are certainly times when you want to light up the distance - so usually one was a powerful thrower. I always found it more convenient to just shift my headlamp around from head to hand as circumstances warranted. This may vary,depending upon how you have the headlamp mounted...