Zatiel did not waste time analyzing the Eternal Darkness' involvement in the Prima-Eldritch Multiversal War. As for a reason, it was very simple. That individual was not in either of the two universes.
What truly mattered to the Neo-Demon were the schemes of the King in Yellow. The ultimate goal of the Eldritch Universe was straightforward: consume the Prima Universe and grow stronger, but there was no way to say how the Eldritch Champion planned to carry on that mission.
No matter how hard he tried or how much time he spent, Zatiel knew he would not be able to figure out the King in Yellow's moves with the information he currently had about him.
The King in Yellow sought to submerge everything into chaos, anarchy, and madness. Still, his wisdom and patience were terrific, so thinking he would make a mistake without external interference was foolish.