The 'style' of Annael's treachery is that Sauron or Thuringwethil visits him at night, and in a trance, he answers their questions and tells them everything they want to know. It's very much 'bewitched by a vampire' type of stuff - maybe some sleepwalking and carrying out tasks, etc.
Basically, Annael doesn't know he's doing these things. He's 'asleep' while it's all happening and has no recollection afterwards. His treachery is uncovered when someone else overhears one of these debriefing meetings, or watches Annael say/do the treacherous thing he's involved in. He hotly denies it at first, but once the witness says exactly what he said/did, he recognizes that just because he doesn't remember doesn't mean it didn't happen...there are gaps in his memory...uh-oh....what did Sauron do to me?!
As far as when it would be useful to have that come out - Sauron's successful military attack at the end of Season 5 does seem to make sense. But it will really depend upon a lot of other things as to *when* we want to get to the reveal of that storyline.
What we currently have for that storyline is:
Rhogrin/Annael/Díriel as captives in Angband
Sauron puts spell-of-not-so-bottomless-dread on some elvish captives
The escape of Rhogrin and Annael and their return to Fingolfin in Mithrim
Annael is visited by Thuringwethil...oh no, he's a spy! (the audience knows, but Annael and the elves remain ignorant)
Annael unwittingly helps Angband in some way
The other elves discover Annael's treachery and reveal it
Annael realizes he is an unwitting mole and there is nothing he can do to stop this. He chooses exile.
We will, of course, have to fit that in with the other storylines of Season 5 and determine which stories it intersects with.