Harris Eggleton was a 23rd century Human male. By the late 2250s, Eggleton was a high-ranking flag officer in Starfleet, serving as the Starfleet Surgeon General at Starfleet Medical until, at least, 2265.
Earlier in his Starfleet career, Eggleton had worked as a medical officer in various deep-space assignments, but had tired of the many problems that could arise with dealing with different alien cultures and the "personalities" of many of his colleagues. In 2258, Eggleton accepted the offer of becoming surgeon general at Starfleet Medical on Earth, where the most contentious thing he had to deal with on a daily basis was a "cranky microbe".
Due to the ill health of his father, Doctor Leonard McCoy transferred to Starfleet Medical under Eggleton's command so that he could remain on Earth and be near his father in his final days. Following the death of his father, Eggleton contacted McCoy and assigned him to a medical relief mission to Capella IV. When McCoy returned from the mission in late 2265, he reported to Eggleton that the Capellans had refused medical aid and that the mission was a waste of time. Eggleton then convinced McCoy that he should remain behind at Starfleet Medical to help to work on a vaccine from choriomeningitis. While McCoy initially agreed, he later accepted a posting to the USS Enterprise as chief medical officer. (TOS - My Brother's Keeper novel: Constitution)