I've gathered a little bit of information on this topic. Bodeker was chief before Eagan's term. He was elected to the position in 1910 and removed from office by Mayor George Ward while he was running for Sheriff in 1914. Ward alleged that Bodeker had taken bribes from bordellos and gambling houses. Bodeker founded the agency that year and was apparently quite successful. In addition to the Birmingham office (in the Brown-Marx Building) and the one Eagan ran in Mobile, there were branches in Charlotte NC, Chattanooga TN, Jacksonville FL, and Montgomery AL.
Eagan's time as chief was short lived. He helped enforce a newly-levied emergency street tax, which was passed when a judge ruled that other earmarked revenues couldn't be used to pay for road bonds. When a white supremacist and anti-Catholic physician, Nathaniel Barrett, was elected Mayor his first official act was to demote Eagen, then the city's highest-ranking Catholic, to patrolman and to elevate fellow Klansman Thomas Shirley to the post of chief. Rather than accept the demotion, Eagan resigned and went to work for Bodeker.
Anything else you've turned up about Eagan would be of interest to me for Bhamwiki.