Just with the time egg, can't it be on that necklace of hers? Like on Kid's neck, there's that shell/wooden looking necklace?
Also, in the good ending FMV, in the end, Schala is standing in "Neo Tokyo" Lol and in her hand we see that necklace that Kid has on her neck. It may be just a reference to the merger that Schala still has a part of Kid, but then again Schala passing the clocks made them turn back, which looks to me as if she has an idea to go back in time or something.