This comes from the RPG, which means it is non-canon. Although we haven´t heard about anything else, I feel safe to say this was what he did during those times

Second War - During the war he had the chance to directly work with Lothar, and once spoke to him about his battle with Medivh. Their knowledge of the terrain and their skill in battle proved invaluable.

After his initial journey he continued his travels around the world, returning to areas he had previously explored, in order to interview members of various races of the world for a history book for school rooms he was considering writing. He put together some of his notes and working drafts concerning the history and culture of each of the Alliance and Horde races, as well as those of furbolgs, Wildhammer dwarves, forest trolls, ogres, and other independent races. He later sent these notes and drafts, including articles on the history and current state of affairs of the Horde and Alliance and other independent organizations, to Ironforge. Around that time, he began to hear rumors of the Twilight's Hammer waiting for C'Thun to rise behind the Scarab Wall in the ancient city of Ahn'Qiraj.

With his new pet ape, Glibb, Brann went back to the southwestern-most wastes of Silithus to investigate the rumors - the discovery of nerubians - as well as learn about the Old God C'Thun and the qiraji from members of the Cenarion Circle. He then set up camp with an expedition in southern Silithus in order to find a way past the Scarab Wall, which he had been to before but had never found a way in. He discovered a silithid tunnel leading into the ancient city of Ahn'Qiraj. Most of his expedition had been killed, but he escaped, leaving Glibb behind, and continued writing notes for his school book. By that time, the Bronze Dragonflight had helped a group of adventurers reconstruct the Scepter of the Shifting Sands, and the gates of Ahn'Qiraj had been opened. Adventurers had just begun to travel into the city in order to defeat C'Thun before he could emerge to devastate Azeroth.