Named for Sam Houston—former Army Commander and President of the Republic of Texas, and Governor of the State of Texas—Brashear was born on July 9, 1866.
Brashear ran for mayor of Houston in 1898, leading a faction of dissident Democrats, while challenging his own uncle, Horace Baldwin Rice.
While Brashear emphasized local control of utilities, he and Rice were similar in background and agreed on important policies, such as advancing aggressive development of the Port of Houston.
John Thomas Browne, a mayor of Houston between 1892 and 1896, formed a slate of candidates and challenged Brashear in 1900.
He was a member of local branches of three fraternal organizations: the Odd Fellows, the Freemasons, and the Sons of the Republic.