Senki Zesshou Symphogear season 1: Does anyone know the name of the track that plays at 23:46 during episode 12?
Boy oh boy do I have a treat for you, my good fellow! The track you're describing is actually a long-intro remix of "Synchrogazer", titled "Synchrogazer -&#x2060;Aufwachen Form&#x2060;-". 

It's no surprise that you had trouble finding it - this remix doesn't actually appear on any of the Symphogear soundtracks! Rather, it's part of Mizuki Nana's album "Rockbound Neighbors". Similarly, her album "Supernal Liberty" comes with another glorious remix titled "Vitalization -&#x2060;Aufwachen Form&#x2060;-". That's the version that plays in episode 13 of G when they all follow the Nephilim into the Treasury. 

(Alas, I don't think either "Exterminate" or "Glorious Break" have analogous remixes.)