Seems to be a lot of evidence that Garmin does not want to implement this feature for some reason. For example, they recently added REM functionality, but it still measures only one sleep period per day. I find this especially mystifying in the context of a company with aviation pretensions, since pilots often have to sleep on erratic schedules. Also internationally questionable when you consider any country with a traditional siesta or daytime nap. In my own case, I think the broken sleep patterns are mostly a function of aging, but I've also noticed that there seems to be a lot of that going around.
To recap, the device should measure several sleep periods per day. My single largest annoyance with the device, and my dissatisfaction is growing over time.