What is the mechanism behind unihemispheric sleep in animals? It is known that dolphins have the ability to sleep with only one half of their brain at a time.

According to this popular science source:


  Dolphins sleep by resting one half of their brain at a time. This is called unihemispheric sleep. The brain waves of captive dolphins that are sleeping show that one side of the dolphin's brain "awake" while the other in a deep sleep ("slow-wave sleep"). Also, during this time, one eye is open (the eye opposite the sleeping half of the brain) while the other is closed. 


Given that the dolphin probably depends on bilateral brainstem mechanisms for respiration, my assumption is that this "shutting down" mainly involves the cortex.  


Is this true, or are areas like the thalamus also suppressed unilaterally?
How is this "switching" (from hemisphere to hemisphere) managed?  Is it accomplished at the level of the thalamus, or within the brainstem?
Were a dolphin to be dominant in one hemisphere (surely Flipper was "right-finned"?), how is the representation of the dominant side of the body managed when the opposite cortex is suppressed?
In general, I don't think the answers to these questions are known.  This paper is a good review of unihemispheric slow-wave sleep (USWS); the section on neurophysiological mechanisms is largely speculation based on how slow-wave sleep is generally thought to function--despite its lack of answers, that section is good reading anyhow, since it covers current evidence (in 2000, anyway!) and lines of inquiry.  I dug through its citing articles as well, hoping for a more informative update; the best I found was this paper, which shows small differences (which may or may not be statistically significant) between the openness of the ipsi &amp; contralateral eyes to the sleeping hemisphere based on right/left--which does suggest at least some hemispheric dominance at play. Eared seals also sleep on their side during USWS, and leave the sleeping side of the body out of the water, while the awake side of the body paddles to keep their nostrils from submerging; I found nothing suggesting hemispheric dominance issues there, though.

As far as hemisphere-switching mechanisms go, that first paper mentions work finding that unihemispheric slow-wave sleep develops only following sagittal transsection of the lower brainstem in cats--even when the interhemispheric commissures were not involved; that implies some kind of uncoupling of lower brainstem sleep regions, but that's about as far as anybody's got (or as far as I could find!).

An interesting question!  If you find more work, come back and tell me about it.

References
1 Rattenborg, Amlaner, &amp; Lima (2000). Behavioral, neurophysiological and evolutionary perspectives on unihemispheric sleep. Neuroscience &amp; Biobehavioral Reviews Volume 24, Issue 8, December 2000, Pages 817–842.
2 Lyamin, O., &amp; al. (2002). Unihemispheric slow wave sleep and the state of the eyes in a white whale. Behavioural Brain Research Volume 129, Issue 1-2, 1 February 2002, Pages 125-129.