This posting applies only in reference to people who are found by conventional polysomnograph (PSG) testing (Zeo would probably find the same) to be sleeping reasonably well, but who insist they can't sleep, or sleep didn't restore them. They are usually called pseudoinsomniacs, sleep hypochondriacs, subjective insomniacs, or sleeping insomniacs. They are typically, for example, prescribed pills and told to stop watching television in their bedrooms.
An article published in "New Scientist" magazine for 14 May 2014, issue 2969 (in libraries, available online to subscribers on the magazine's Web site, and findable elsewhere by its Web title "Awake asleep: Insomniac brains that can't switch off" (e.g.
http://stirling-westrup-tt.blogspot.co.uk/2014/05/tt-ns-2969-awake-asleep-insomniac.html, though this doesn't include the important graphs) describes some recent work. Basically we know sleep is distinguished into several phases, detected largely by brain-wave characteristics. Wakefulness has waves of short wavelength and lower amplitude; restorative deep sleep has much longer waves of larger amplitude (delta waves), and so on. Analysis has involved an expert looking at rolls of PSG output, characterising the phases of sleep, and adding up the time in each.
The new analysis involves nothing more complex that normal mathematical periodical wave analysis (spectrum analysis). On looking closely at the delta waves of pseudoinsomniacs only, the long delta waves can be seen to have bursts of short, lower-amplitude, beta waves superimposed on them, intrusions. Fourier analysis (viewing not amplitude as a function of time, but the frequencies present and their amplitudes) confirms and quantifies this. Their trouble is not that their sleep is insufficient, but when they sleep their brains are not quite switched off. Awake or not, around the clock their brains showed more activity than normal sleepers. They were also found to pick up new tasks more quickly than normal, rested, sleepers.
Going a bit wider, alpha intrusions seem to correlate with many problems unrelated to sleep: chronic pain, chronic fatigue, depression, PTSD, and in the sleep of people with fibromyalgia, which causes chronic pain.
The article goes on to discuss possible explanations, and treatments being tested.
I don't know enough about Zeo to know if, even in principle, a Zeo with RS232 output could show any of this. It would certainly involve spectrum analysis software (analysis modules are easily available, though).
I hope this is of interest, best wishes.