My guess is that reverse blinking is a form of focused attention which helps keep the sleeper from engaging in thoughts that keep them awake by occupying the required attention for this with a simple and repetitive task that is easy to do, yet isn't so boring that the person is demotivated to keep doing it.

As for research and studies to back this up, I couldn't find any on reverse blinking specifically, but I found some on other cognitive tasks done while falling asleep. Reverse blinking is a cognitive task done while falling asleep so I think these studies referenced in the following link are relevant, especially on the second page. (https://pdfs.semanticscholar.org/cbf...ccd9241d74.pdf)