Board Thread:Theories and Speculation/@comment-734582-20150712141917/@comment-6769189-20150914040443

The way I see it is this:

Kaguya got the RinneSharingan from the Shinju. We seen that the Shinju has effects on ones body in shape or another, it also changed her normal eyes by giving her Byakugan abilities. Pretty sure that before the Shinju her eyes were nothing special. Technically, she has 6 Paths chakra and some form of senjutsu(at least after absorbing the Shinju). Her power was split among her sons.
 * Both received 6 Paths Chakra. How/when either of them gained Senjutsu is unknown.
 * Hagoromo: Recieved the Rinnegan and its abilities. He probably didn't have the Sharingan because he was genetically predisposed to the next evolutionary step.
 * Hamura received the Byakugan and bone stuff(maybe)

Kaguya didn't get the Tenseigan because, biologically speaking, she didn't need it. She had the Rinne Sharingan took care of just about all of her needs. Kind of like a Natural Selection thing. However this doesn't mean she didn't have the potential.

So all in all, if Hamura became the TT-Jin, it may have pushed his Byakugan to the next level into the Tenseigan, and going by your guys' descriptions, would have given him his own 6 Paths, allowing him to become the Sage of 6 Paths.