Yes that seems most likely, the other ones evolved from that original eye. But it got so confusing near the end and all about the Otsutsuki's is confusing to me.
Hagoromo 3rd eye was the first. From it came Juubi(God tree). From Juubi came Rinne sharingan. From Rinne sharingan came Rinnegan + Sharingan. Byakugan is just a derivation of the above two eyes which might explain the fact why they got no offensive abilities. It's more of a 'stripped off' eye, akin to a residue of a polished metal.
Yes that seems most likely, the other ones evolved from that original eye. But it got so confusing near the end and all about the Otsutsuki's is confusing to me.
It should be that way, it is why Sharingan is actually more haxed then Byakugan itsself because it has the power of Rinnesharingan and it can mutate into further stages - The thing about Otsutsuki confusing you?
As far as we know, byakugan (or at least white eyes) predate the rinne sharingan, which then predates both the rinnegan and the sharingan. This is the case at least for Kaguya and her descendants. The thing about it is, we don't know if Kaguya could actually activate her byakugan before eating the fruit. In the anime, she actually showed some strange repulsion power that seemed to stem from her byakugan, and this was before she ate the fruit. However, we didn't see her using the usual long distance x-ray vision abilities until after eating the fruit.
On Earth then, the order of emergence goes:
Byakugan
Rinne sharingan
Rinnegan (If you don't count Hagoromo's anime only awakening of the sharingan)
Sharingan (unless you count Hagoromo's sharingan, in which case it would be sharingan before rinnegan)
That is on Earth though. In space, we get into more unknown territory. For example, we don't know if Momoshiki was born with the rinnegan or if he got it from fruit. We also don't know what kind of KKG other unknown Otsutsukis may have. There are also other lesser known dojutsus that pertain to the Otsutsuki such as the tenseigan and the jogan.
Edit: Then there's the fact that Momoshiki probably had the best rinnegan before Kaguya ate the fruit, which would make rinnegan come before rinnesharingan in that case.
Hagoromo 3rd eye was the first. From it came Juubi(God tree). From Juubi came Rinne sharingan. From Rinne sharingan came Rinnegan + Sharingan. Byakugan is just a derivation of the above two eyes which might explain the fact why they got no offensive abilities. It's more of a 'stripped off' eye, akin to a residue of a polished metal.
The thing on his forehead is a chakra mark, much like Hashirama's and Tsunade's
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Mind you, in order to obtain the rinnesharingan, you first must have both the chakra and the vessel (which is the overall theme of the arc) Yang = vessel = physical = body. Yin = chakra = spiritual = mind.
Kaguya was split. Her vessel was entombed in the moon while her chakra was sealed within Hagoromo until he split it into 9 portions, creating the bijuus.
Obito and Madara never gained the 3rd eye when they absorbed the juubi. Only when Madara took the vessel of the godtree were he been able to complete the vessel and chakra gaining him to unlock the 3rd eye and thus becoming a host for Kaguya's revival.
How would Hagoromo even unlock them without those? Remember, Hagoromo is the Yin (with the Yang seal)..
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He was never BOTH Yin and Yang.
In order to be both, he'd have to retrieve the perfect vessel from the moon. I say perfect because for some reason the gedo mazou became detached to the lotus flower/godtree after old Madara's death.
Again, he and Hamura were only 2 sides.. Just the Yin or Yang (with the seal to symbolize the whole Yin within Yang and vice versa).
Hagoromo were never both. Meaning he never had the 3rd eye.
Also, that's not the 3rd eye he has on his forehead. Just a seal mate.
yeah, people mistake his forehead seal as the 3rd eye or that they argue that he sealed his rinnesharingan but it isn't the case as he already had it before Kaguya was sealed and that it has been established by the manga that you need more than the juubi to unlock it as Obito and pre-godtree Madara never had it.
Reviewing Logic had a good question an it could be that this fruit is on their home world an sucked it dry, but not before they harvest seeds from the fruit to disperse throughout the cosmos..
The fruit gives them extra power on top of what they already wield.. (Byakugan) Mutations from the tree's fruit gives them Rinnegan with it's special properties, Sharingan & it's special properties & Tensigan with it's properties..
All of them have their ups/downs/pros/cons, so doujutsu wise it's the Byakugan which is wielded by the clan then considering the person & skill they could get the other mutations like Rinnegan,Tenseigan & Sharingan by means of the fruit.. I'm not sure if Otsutsuki lineage members are born with anything outside the Byakugan unless Boruto counts with his Jougan..