My actual theory is that he rests like a dolphin. Dolphins can’t sleep because they’re mammals and would drown. So they rest one half of their brain at a time. I’m no marine biologist, so I probably botched that description.
With people, only the left half of the brain is capable of speech. Here’s where I totally depart from science, but my idea is the left hemisphere is “ME”, i’m the person talking. The right half thinks but never speaks, so I think of it as subconscious. People have two brains, and some people only have one, there‘s a procedure called a hemispherectomy in people with seizures where they remove or somehow disable half of the brain. So what I presume is Jack’s brain halves are tag teaming the job of being Jack.
I’m sure that‘s very uninformative, but I thought it was an interesting question so I took a whack at it.