Elidibus has never explained what he is actually doing. At least, not well. When he is first introduced in 2.1, he says that if Minfilia were to learn... something... then he and the Scions would be on the same side. And then never tells Minfilia what that something is. He never does end up explaining what he is really up to either. Of course, the one time someone (Urianger) did know what he was talking about, Urianger turned the tables on Elidibus and stopped him from influencing the WoD to kill the WoL and kickstart another Calamaity. It's only after that does Elidibus start taking a more active roll in events. I can easily see Elidibus not telling people things because they might want to mess what he is doing up.

Solus is a lot less cagey. He's got a taste for the dramatic and loves monologing about what he is up too. He even goes so far as to explain his reasoning to Varis when Varis gets it wrong. I have a hard time seeing him not explain himself to the WoL either.