You can determine your longitude without a clock, but achieving precision with this method is challenging. First, you need to observe the Moon's position relative to fixed stars, which gives you the UTC time. Then, observe the Sun's position relative to the horizon to determine the local time. By comparing the two, you can calculate your longitude.
How are you going to usefully use this information if you wouldn't have an obvious way to know precisely how long it's been between whenever you lost track of the moon and stars and whenever the sun is clearly visible over the horizon?
