I read on HN that they found islands over the horizon by looking at patterns in the waves and navigated by memorizing the position of stars. Yes to the harvesting of rain water.
I'm curious as to the range that these things could be detected. No doubt there's some proportionality between island size and distance-detectability.
But there are a whole bunch (small) islands in the middle of a whole lot of nothing, so I'm curious to know how many were found on purpose and how many by accident.