Henry Adams Thompson was born 23 March 1837. He was a native of Pennsylvania but spent much of his life in Ohio. He became a member of the United Brethren Church and taught mathematics at several United Brethren colleges in the Midwest, eventually becoming president of Otterbein University (1872-1886). Much of his time as college president was devoted to improving the financial standing of the school during the economic depression which followed the Panic of 1873.
Initially a Republican, Thompson joined the Prohibition Party in 1874 and ran for several offices on that ticket. He was unsuccessful as a candidate for Congress in the 12th District of Ohio in 1874. He served as chairman of the 1876 Prohibition Party National Convention, in Cleveland. Four years later, he was nominated to be the Party's vice-presidential candidate, joining the ticket with Neal Dow. That ticket received more than 10,000 votes.
In 1887, he was nominated to be the Party's candidate for governor of Ohio; he placed 5th. Thompson would run for Congress several more times and made his best showing running for the 4th District in Indiana, winning 2.24% of that vote.
Henry Thompson died in Dayton, Ohio on 8 July 1920 and was buried in the Otterbein Cemetery in Westerville.
-- Data from Wikipedia
nb: The Indiana Thompson was Samuel, not Henry.