By trade, Gajic was an accountant. He had married a woman named Sarah and had two daughters with her. One time while on a family vacation to Mars, the ground collapsed beneath the rover they were on. Gajic woke up to find out his family had been killed in the accident. After taking leave, he returned to work, but found his heart was no longer in accounting.
Encountering a man who said he was the last of his order, Gajic learned about the man's quest to find the Holy Grail used by Jesus Christ at the last supper. Before dying this man had told Aldous he was a good person with unlimited potential. After the man died Aldous inherited the man's staff and resources, and took up the man's quest to find the Holy Grail.
In 2258 his quest took him to Babylon 5, where he met with each of the ambassadors to see if they could help him find the grail. Delenn and Lennier held Gajic in high esteem as he was a true seeker in their eyes. Delenn had sent word home of Gajic's request for information on the Holy Grail, and that request was disseminated throughout the Minbari. The other ambassadors were not able to help though.
Meanwhile after a young former construction worker named Thomas Jordan a.k.a. "Jinxo" had been caught in the act of trying to pick Gajic's pockets, Gajic offered to the B5 ombudsman to take the younger man under his wing. Jordan could not believe that Gajic was being so nice to him, and felt that he had been cursed as he had worked on the previous Babylon stations before they were destroyed or disappeared. He also had difficulty with the concept of the Holy Grail.
Gajic died when he was caught in the crossfire between a Downbelow boss named Deuce and station security. Before he passed he bequeathed his staff and his order's resources to Jordan. As he laid dying Gajic told Jordan that he could see the Holy Grail.
A short time later Jordan left Babylon 5 with his friend's remains, in order to see him home to Earth, before continuing his friend's quest. As Jordan prepared to leave, Delenn gave him a crystal to crush into the ground after Gajic was laid to rest, explaining the crystal would glow each night for 100 years, and that it was the Minbari way of honoring true seekers.