Some preliminary conclusions

It is not that easy to determine the REM phase from motion data. unless you want to try to predict it, and especially that during REM "Limbs are totally still".
Last advances in the LD direction was last night, After detecting total stillness of the hand, start flashing the flash with predefined intervals (5 minutes). When motion is detected again, delay flashing for 7 minutes and then continue. Here is the chart of motion data and flashing times.
The flash flashed 58 times last night, I noticed 1 of them.. since the flash is on my hand not pointing at my eyes, it might go unnoticed.. I am thinking about playing a certain sound or vibrating instead.. like here
On the contrary, REM can be detected by the varying breathing rate as seen here. But it is much easier to attach the phone to your hand instead of your chest..