Naruto is a very likely character. Given his strong will and connection to the Nine - Tails, he would be motivated to time - travel to fix problems related to the Juubi. His ability to make friends and influence people would also play a big role in any time - traveling story.
Naruto would likely be one of the main characters. Since it's a Naruto - centered fanfiction, he'd be the one using the Juubi eye for time travel, probably to save the world or his friends. Sasuke could also be involved. Maybe he initially opposes Naruto's use of the Juubi eye for time travel but later realizes its importance. And there could be villains like Kaguya who might try to stop Naruto from using the Juubi eye's time - travel powers for their own evil purposes.
Shinji is a very likely character. His complex relationship with his father and his role as the main pilot make him a prime candidate for time travel scenarios. He could go back in time to try and fix things or understand his father better.
Artemis could be involved as well. Her skills as an archer and her family's complex history could lead to some interesting time - travel scenarios. For example, she could travel back in time to discover secrets about her family's past that have an impact on her present - day self and the Young Justice team.
Izuku Midoriya is a likely candidate. His strong sense of justice and his journey to become the greatest hero make him a prime character for time - travel scenarios. He might travel back in time to gain more knowledge or to prevent certain tragedies. Another one could be All Might. His past is full of secrets and his influence on the hero world is huge. Time travel could be used to explore more of his backstory or to change some crucial events in his past.
Obviously, Stan, Kyle, Cartman and Kenny are the most likely. They're always at the center of the action in South Park. Their different personalities would lead to really interesting time - travel scenarios. Stan's more level - headed nature might be the voice of reason during time - travel chaos. Cartman would probably be trying to use time travel to his own greedy advantage, like finding a way to hoard all the cheesepuffs in history.
Katsuki Bakugo, with his powerful quirk and complex personality, could be a character in time travel fanfics. He might go back in time to prove himself even more or to change certain interactions he had with other characters in the past.
Lelouch is a very likely candidate. Given his intelligence and his desire to change the world, time travel could be a means for him to correct past mistakes or gain more power to overthrow Britannia. Another one could be Suzaku. He has a strong sense of justice and might use time travel to prevent some of the tragedies that occurred.
Morgana might also be involved. If she were to travel through time, she could either try to change the past to gain more power in the present or she could be sent to the future to see the consequences of her actions. This might lead to a change of heart for her, or it could make her more determined to achieve her goals depending on what she witnesses.
Marco would also be likely. He's always been by Star's side, and his strategic thinking could come in handy when navigating the complex situations that time travel presents. Plus, his relationship with Star means he would be motivated to go on these adventures with her.
Obviously, Naruto would be the central character as it's about his reincarnation of Juubi. Sasuke would also play a major role. He has always been Naruto's rival and friend, and in this scenario, he would be involved in Naruto's journey with the new power. Kakashi could also be an important character, perhaps guiding Naruto in some way on how to handle this new and dangerous power.