I agree on the efficacy of a strobe, but don't carry a dedicated unit. I too have a Princeton Tec EOS which has a strobe function as do several other headlamps. But for EDC, all of our family members carry Photon Freedom Micro LED keychain lights in multiple places (keys, zipper pulls, etc.). The Photons include a SOS mode and carrying several provides redundancy. The Photons are not waterproof however we've soaked them many times and when they dry out they work again. The brighter the better but there is anecdotal news that even the weakest light source can be effective - remember the story of the climber aiming his cell phone display at a search helicopter who did spot it? And we know a flashing source is more effective than a steady light.
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Men have become the tools of their tools.
Henry David Thoreau