As mentioned a couple of days ago, I did, indeed, read through Rambam's Hilkhos De'os, searching for statements on sleep. This is part of a larger project on my behalf to look into perspectives on sleep in Judaism (I have posted earlier on sleep statements in the Yerushalmi.) After having done so, I ran a Bar-Ilan search and found some more מקורות (sources) for Rambam's view(s) on sleep. However, I have yet to look more into those results and will do so later.
Most of his statements concerning sleep are to be found in chapter four, but there a couple elsewhere, too. His statements on sleep fall into three categories: 1) Statements directly from the Talmudic sages, 2) Statements expanding upon Talmudic statements, and 3) Original statements of his. An instance of each of these is 4.5, where a direct one is לא יישן אדם לא על פניו, ולא על עורפו, אלא על צידו from Berakhos 13b and Niddah 14a, an expansion on that is that which follows: בתחילת הלילה על צד שמאל, ובסוף הלילה על צד ימין, and the latter part of that statement is original material: ולא יישן סמוך לאכילה, אלא ימתין אחר אכילה כמו שלוש או ארבע שעות. ולא יישן ביום. Also known in this last category is the previous line, which is rather famous: דיי לו לאדם לישן שלישן, שהוא שמונה שעות; ויהיו בסוף הלילה, כדי שיהא מתחילת שינתו עד שתעלה השמש שמונה שעות, ונמצא עומד ממיטתו, קודם שתעלה ,השמש found in 4.4.
Although I still have to look throughout for sources in the Mishneh Torah, I was wondering if he has any sleep statements in the Guide to the Perplexed. Of course, I am aware of his famous letter where he states he is so busy throughout the day and needs help getting into bed he is so tired at the end of the day.
(Translations of the above: A man (I think this is specific to men (see Rashi on Berakhos 13b and Niddah 14a), unless this is not due to fears of erections, in which case I am open to hearing other suggestions.) should neither sleep on his front, nor on his back, but rather on his side. In the beginning of the night on his left side, and in the end of the night on his right side. He should sleep close to eating, but he should wait until after eating, like three or four hours. And he shouldn't sleep during the day. It is sufficient for a man (okay, this one ought to be more properly translated as 'person') to sleep a third [of a day], which is eight hours, and it should be at the end of the night, so that from the beginning of his sleep until the sun rises would be eight hours, and it would be found that he is standing from his bed before the rising of the sun.)