"Eventually" is more likely to be later than sooner. Having to rely on them slipping up is enough of a problem already.

[It's not difficult to tell from the touch of sourness in his tone that Shun despises having to rely on his enemy for anything, even if it's something like leaving a trace so they can be tracked down and stopped.]

We had someone announce their intentions to bring down the Heavens and Amaterasu a few weeks before. There could be multiple parties, but when we don't even have one pinned down to blame for any of these attacks, it's better to focus on the one and go from there.