This is the tough question.
The best way we can look for reincarnations of Indra is to find strong Uchiha who had a strong rival (Senju). I would say both Madara and Sasuke are descendants. Madara showed it as Hashirama's rival. This naturally passed down to Sasuke who is Naruto's rival.
We now have to ask why this happened to Sasuke, and it wasn't Itachi as the trait seemingly befalls older brothers (Indra and Madara). The answer IMO is due to Madara extending his life. We know Fugaku (Sasuke's father) was the leader of the clan similarly to Madara. We also know Sasuke looks a lot like Izuna. This likely suggest a direct blood line between Sasuke and Madara, and probably Sasuke and Indra. Since Indra cannot reincarnate until he dies again, this ultimately leads to Sasuke being the reincarnation.
As we know, Madara managed to extend his life up until the arrival of Obito. He dies when Obito is roughly 15 (he unplugs himself). Itachi is about 8 years younger than Obito (based on Kakashi's age). So when Obito is 15, Itachi is roughly 7 years old during Kurama's attack, and thus Itachi was already born before Indra could reincarnate.
We also know that some time passed between Madara dying and Obito attacking Konoha. This gives us about a year or two max in terms of time.... which means Itachi had already been born, but Sasuke was not (him being born just ahead of Naruto [August being Sasuke; November for Naruto]. Thus, Madara's death coincides within a relatively close time frame to Sasuke being born.
This explains why a younger brother was the reincarnation. If we continue with the Elder and Younger analogy throughout the series... the Elder has been depicted as cruel or evil (Itachi's introduction and clan massacre starting off as a villainous person). So we can assume the fact Sasuke was the will but in a younger son family position... it is a sign that the Cycle of Hatred will be broken.
As for the question of Souls, I would say you're thinking about it the wrong way. I'll use Tokyo Ravens as an example. In the manga/anime Tokyo Ravens, there is a descendant of a legendary Mage. This individual ends up basically saying this: I may be this Mage's reincarnation, but I am also me.
In short, while you are the reincarnation of someone, you exist as your own entity as well. This is best explained using Greek Mythology.
When people in Greek Mythology die, they'd go to the Underworld ruled by Hades. They'd travel down the river of Acheron. Long story short, before they are to go be reborn, one must drink from the river of Lethe to forget their past memories. Only then can they be reincarnated.
With that, you should think of reincarnation like that of Avatar the Last Airbender. It isn't the same spirit being reborn per say. Instead, it is more like a new individual is born, but were they capable of remembering their past lives, each new reincarnation would be themselves plus everyone behind them.
So Madara would be his previous forms and Indra. Sasuke would be Madara and Madara's previous forms up until Indra.
To conclude, there is no split between souls. They are two different souls, and are simply linked through the concept of time. Sasuke standing at the front, linked behind him is Madara, who knows how many people, and then Indra at the far end of the link.
