No pictures of him had ever been published and he had an extreme distrust of telepaths. Even going so far as to force Garibaldi to fire Lyta Alexander whom he had hired to assist him in his work.  By his own secret admition, he along with several other wealthy and powerful individuals were in fact the "real leaders" in control of the Earth Alliance, operating as a kind of shadow council. Additionally, his feelings towards the Clark regime were essientally neutral. He agreed, that while, Clark and his associates were a problem that in a few years time they would be gone by nature of the political process and that because he as a wealthy and influential person was not being adversely effected. He also gently hinted that he and his wealthy friends would have a hand in choosing the next administration. 
When Michael Garibaldi goes to work for Edgars he reveals, alongside with one of his employees, Wade, that he has genetically engineered a virus that attacks only telepaths. Due to the distrust and apparent risk of telepaths gaining control over the Earth Alliance, a means of controlling a telepathic coup had to be developed. The virus, both airborne and extremely contagious, would infect those carrying the telepathic gene and kill them unless they received injections of a developed antidote every two weeks for the rest of their lives. Unknown to both Garibaldi and Edgars, Garibaldi was a programmed sleeper agent for Bester and the Psi Corps, who subsequently relayed this information along.
Soon afterwards William Edgars was killed at his Mars home and office by agents of the Psi Corps, where the virus and cure were stolen.