The Boruto anime has showcased the protagonist's Jogan on multiple occasions. But that isn't the case for the manga as it has yet to see the dojutsu make its debut in a scene other than that of the flash-forward. In contrast, Kawaki's dojutsu Kokugan has appeared in both anime and manga.
This different pace of development for both characters suggests that the two dojutsu have no connection with one another. However, that might not be entirely true as one theory suggests that the two dojutsu might have originated from the same being. The same has been hinted at by Boruto and Kawaki's karmic resonance.
Disclaimer: This article may contain spoilers from the Boruto manga.
Boruto and Kawaki's dojutsu may have originated from Shibai
As per a theory by a fan on Reddit u/ILOVEcBJS, Boruto's Jogan and Kawaki's Kokugan may have originated from Shibai. This might be why their karma resonate so much with one another.
While it is quite known that Shibai Otsutsuki possessed Rinnegan, Senrigan, and Byakugan, as per Amado's explanation, transplanting DNA harvested from Shibai's remains results in the endowing "one or more of his abilities." This means that transplanting Shibai's remains did not necessarily mean the manifestation of the Otsutsuki God's powers, but also some new powers
This has also been implied by the known origins of Kawaki and Boruto's dojutsu. The Kokugan is a dojutsu Kawaki inherited from Isshiki Otsutsuki. As for Jogan, Momoshiki Otsutsuki implied that the dojutsu belonged to the Otsutsuki clan.
As far as one can theorize, Isshiki Otsutsuki may have had two Byakugan eyes but might have acquired Kokugan from Shibai after Amado transplanted the Otsutsuki God's remains onto him.
This development is also close to Kawaki's nature as he is power-hungry like Isshiki. Rather than choosing the Shinobi route, Kawaki relied on Amado to give him upgrades. Thus, there is a chance that Isshiki must have also taken the same route and had Amado modify him.
As for Boruto, the reason he has yet to manifest his dojutsu in the manga might be due to his decision to take the hard road as an outcast shinobi. He trained daily for three years and refused to use his karma during his fights. This might be why, despite possessing the dojutsu, he has yet to manifest it in the manga.
While the clear origins of the same cannot be deduced, there is a good chance that Boruto and Kawaki's dojutsu are connected to Shibai in some way, causing their karma to resonate.
Lastly, there is Code with the White Karma, who could represent the rest of Shibai's body separate from the head. This might be why he can create Claw Marks and imbue his chakra onto the Ten Tails to create the Claw Grimes, which can later turn into God Trees upon biting someone.
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