Let's suppose you can travel back in time by passing your state of mind/memories to your former self. You go back to your former self who has slept some hours ago, a day passes without sleeping and you travel back in time again, and you repeat this process dozens of times (presumably to try to change an event you dont want to happen) . Would your former self have the accumulated tiredness of dozens of days (needing to sleep) or since the body of your former self slept a few hours ago would you feel energetic without needing to sleep all the time?
This is a wonderful opportunity to give your science fiction story a bigger science than we currently possess. We have no minds that are independent of the bodies they are currently attached to, so we have no way of testing whether mental weariness is separate and distinct from physical weariness.
I have personally noticed that my mind slows down after 16-18 hours of concentration, but the timing of that slow down is suspiciously close to other symptoms of physical tiredness such as muscle tightening, yawning, and gradually increasing eyelid weight. I cannot empirically determine whether two simultaneous events are occurring (separate physical and mental tiring) or if it is a single event with multiple distinct symptoms.
Your time traveler has an opportunity to learn what we do not know. Does the mind tire separately from the body?
So choose whichever "truth" serves your story best and run with it.