Board Thread:Theories and Speculation/@comment-26889573-20151008053113/@comment-6769189-20151021010441

If the Otsutsuki eyes were brown, the Byakugan would be brown. If otsutsuki eyes were yellow, the Byakugan would be yellow. However, ots entirely possible the Shinju made the eyes white, since we never see an Otsutsuki pre-chakra, though considering Himawari, this might not be the case. Having Byakugan pre-chakra makes no sense, since its abilities are activated by chakra and one of its highest coveted abilities is to see chakra.

The Shinju from Momoshiki's world was weak and drained. I don't think it said whether or not they got their power directly from it. After Momoshiki and Kinshinki combined he got a 3rd eye.