The mechanism would be inside the waterproof watch case but would make it ridiculously chunky. I have two Seiko watches, one is solar and the other mechanical. The mechanical one weighs more and is chunkier. Solar only just works enough to keep the other watch going during the Winter and that's with me shoving it under a bedside lamp in the evenings too. If the OP is hellbent on solar power they could do worse than invest in a solar panel equipped portable charger which they can leave on a windowsill during the day and then charge the watch from it at night. Obviously it wouldn't monitor sleep patterns that way but to be honest, you either sleep or not. So those sleep functions are a gimmick and cannot help you sleep better
