In short, whatever alignment tgk flips, we get about the same amount of "info".
I'd sorta disagree. TGK gives some form of info on me (pushing him more than SS), SS (still is the other lynch option), Celever (defending more), Camo (seemingly ignoring the TGK option), and ultimately everyone who votes for them. And any role claim he makes.
SS gives some info on the same people as TGK (Camo, Celever, me, TGK, people who vote for him), obviously, as well as IE/EM if suspicions are correct. And those who were keen to vote for him early on. Definitely more information there, but I wouldn't write off the info that can be gotten from TGK.