As a former dolphin researcher at the Kewalo Basin Marine Mammal Laboratory of the University of Hawaii I can say that we've known about split brain sleeping for at least three decades. I had always wanted to run an experiment looking for an acoustic equivalent to Rapid Eye Movement in dolphins. It could still be called REM sleep just substituting Eye with Echolocation. Since you really don't want to attach EKG leads to a swimming dolphin we'd have needed a set of directional hydrophones arrayed around the tank who's data would be correlated with the dolphin's head position as it swam. Perhaps this could be tackled now but back in the day it was beyond us.