I recently learned the rudiments of celestial navigation, and have been pondering its three basic requirements: a clock, a book of star positions, and a sextant (or device for measuring star inclination).
It got me wondering if someone, classically "trapped on a desert island", could sufficiently observe the stars and write a message-in-a-bottle that would, if picked up, lead rescuers to them if they didn't have any of the necessary items when they landed there (never mind the likelihood of any of these things occurring).
The sextant can be crafted from local items (a couple sticks, a rock, some string, and a fair bit of math), so that's available. Without the book of star positions, the castaway could record his observations and let the message-finders use their book to figure out his location. But that leaves the clock; time is a key element of the data needed to use celestial navigation, at least the way it's classically done.
So, the question is two-pronged: how can you tell time at night with some measure of accuracy? and what methods of star observation are useful for determining position without knowing the time?