Obito also extracted half of the Nine Tails for Naruto, which is how he ended up meeting Hagoromo.

This is confirmed later by Kakashi when he got taken over by Obito. Naruto first got Six Paths Chakra from Obito, whom extracted a small amount of Six Paths Sage Chakra from Madara. By receiving all of Hagoromo's chakra, he possess the same element that makes Kurama the only Bijuu that has an avatar instead of Bijuu transformation. Lastly, this also explains how Ashura had a KCM-like yellow avatar that does not look like Kurama.

So instead of Six Paths Sage Mode, it could be more appropriately named Sage of Six Paths Mode (both translates to Rikudou Sennin Modo) as in 'Hagoromo mode', the difference being the Kyuubi Chakra. This is because the chakra the Yang seal supplies contains Kyuubi chakra as well. Naruto with just base Six Paths Sage Mode had the fox-slitted pupils in his eyes, even without direct link to Kurama. The number of Bijuu (Gedo Mazo included) corresponds to the number of TSB awakened.ДЄt this point, Hagoromo's chakra already contains that of the Nine Tails. Truth Seeking Orbs are awakened by Jinchurikis with Six Paths Sage Chakra. This also explains how Hagoromo possessed one TSB prior to becoming the Juubi Jinchuriki. However after he exhasted all of the Kyuubi Chakra left in his body, he no longer see Hagoromo, even though he continue to replenish Six Paths Chakra. And after he got Hashirama's cells from Kabuto, the Six Paths chakra mixes with the Kyuubi chakra to create Hagoromo's chakra. Sasuke was also able to meet Hagoromo due to the small amount of Kyuubi Chakra he received from Naruto. This explains why Hagoromo was not able to manifest in Madara's mind when he awakened the Rinnegan, and also why Sasuke was able to awaken Rinne Sharingan but Madara didn't. According to Hagoromo himself, his chakra not only consist of the chakra of Indra and Ashura, but also that of the Kyuubi. Six Paths Chakra is not the same as Hagoromo's (base/pre-sage) Chakra as it is only part of it. By absorbing the chakra of all nine Bijuu and Gedo Mazo (i.e. By mixing the chakra of Indra and Ashura (i.e. There are three ways to obtain Six Paths Chakra:ДЎ. Six Paths Chakra is the source of the Six Paths Powers, such as awakening the Rinnegan or Six Paths Senjutsu.

Naruto sage of six paths