I tried this technique for about five nights when I was going through a particularly stressful period, and honestly, it made me feel more awake, not less. The deliberate eye movement seemed to activate my brain rather than calm it--I'd lie there rolling my eyes around and suddenly start thinking about all the things I hadn't done that day. I gave up because I realized I was creating more mental stimulation when what I actually needed was to quiet my mind; I went back to my breath work and gratitude practice before bed, which helps me address the root cause of my restlessness rather than just trying to trick my body into sleep.
After six nights of giving that viral trick a fair shot, I realized I was just perfecting the art of staying awake with style. The constant rolling made my eyes feel like they were training for a gymnastics event. To calm myself, I listen to slow instrumental music and relax every muscle in my body one by one until I drift off to sleep.