Technically Zombies don’t sleep nor do they need to sleep since they’re dead. However a zombie horde will cease mindless movement after a certain amount of time without spotting, or smelling any human, or animal prey. Plausibly due to the zombie virus weakening without sustenance. It then goes into a state of temporary stasis. They will remain standing still with their heads hanging down until something disturbs them. Zombies that wander off alone will eventually collapse, and appear truly dead if no prey or other zombies are seen after a period of time. However they’ll pop back up again the minute they smell or hear any humans, animals, or zombies. Sometimes weather conditions including a brisk wind will get them re-animated. Never assume that a motionless zombie lying on the ground is harmless. Destroy the brain, and ask questions later.
If faced with a natural or artificial obstacle, such as a fence, they will continue to move against it if prey is on the other side. Within hours they will cease movement if unsuccessful in conquering said obstacle. Once the object of their fascination is gone they will turn left or right, or all the way around to stagger back where they came from. Without any prey to guide them the most common direction is to turn left for reasons unknown. Clearly there is no zombie horde leader so it is unknown what guides their travel when no evidence of human prey, or even interesting smells exist. We do know that they tend to follow the path of least resistance.
On a related note I’m Mystic Investigations half zombie Cryptozoologist Ashley Abercrombie. Commonly a Zombie-Human Hybrid is known as a Demi-Zombie. I personally only sleep 3-4 hours a night. However I’ve gone a week with only 2 hours of sleep per night. Clearly that’s all my human half needs despite the average adult requiring 7-8 hours of sleep on a nightly basis. I’ve been told that indulging in my craving for human flesh would greatly eliminate my need for sleep but I refuse to give in to my dark zombie desires! You can find short stories featuring me here.