When Rush found the bridge, the hallucination of Gloria appeared to him, aware that he had no intention of revealing his discovery to the rest of the crew. She seems to exist to second-guess Rush's decisions, as well as recommend that he take care of himself. She is unhelpful with scientific matters, and ignores Rush's requests to let him speak to the hallucination of Jeremy Franklin. (SGU: "Aftermath", "Awakening", "Pathogen")
With the recent discovery that the Jeremy Franklin 'hallucination' is actually the remnants of Franklin's consciousness that were uploaded into Destiny's database when he used the interface chair (SGU: "Hope"), it is unclear whether Destiny was able to create the Gloria hallucination based on the memories it acquired from Rush during his own experience in the chair or if- given the more personal advice she offers Rush- she is just a conventional hallucination.