The text is called Sfat Emet Siftei Kohen (שפת אמת שפתי כהן), and it was authored by R' Bentzion HaKohen. You can find copies for purchase here and here, although I regret that it's nearly impossible to find anything about it. It has nothing to do with the Gerrer Rebbe, and the pronunciation for which it serves as a guide has nothing to do with Gerrer pronunciation. On the contrary, he seems to advocate an approximation of an eastern pronunciation (Teimani, Baghdadi, etc), and devotes a great deal of attention to carefully explicating every letter and every vowel. It's ironic, therefore, that some people might refer to it as Sefer Sefas Emes, since this is the very pronunciation that its author is militating against!
My only source for all of this is the fact that I've flicked through it, briefly. I do not own it, nor have I succeeded in finding anything useful about it online.