To quote from a speech made by Andrew Merrilees to the Head of the Lake Historical Society on December 15, 1968:
The one man who more than anyone else was responsible for [the TH&B's] promotion and construction, and who for many years was in charge of its operations was the late Mr. John Newton Beckley of Rochester, New York. Mr. Beckley was president of the Dominion Construction Company, which promoted, built, and operated the line for a short time. He was elected president of the TH&B on January 1, 1897. Mr. Beckley was a prominent Rochester lawyer and industrialist, and in addition to being president of the TH&B, was at various times president of the Rochester Railway Company, which was the city street car system [...] and of the General Railway Signal Co. of Rochester, which was, and remains today, one of the two largest firms manufacturing railway signalling devices in the United States.
The railway began operations on December 30, 1895, and a brief period of operational independence, the company was managed by the Michigan Central Railroad (the person in direct charge of operations was General Superintendent R.H. L'Hommedieu). The MCR left only one senior manager in residence in Hamilton, Superindendent J.B. Morford, accompanied by an experienced MCR Trainmaster. After about eighteen months, the MCR withdrew from this responsibility and control returned to Hamilton. The new General Superintendent and Chief Engineer was Elstner Fisher, who had been an Assistant Superintendent on the MCR. The presidency, as noted above, passed to Mr. Beckley.
Beckley remained TH&B president until his death in 1933. There is a photograph of Beckley on page 67 of Norman Helm's Shadow. Helm goes into great detail on the activities of President Beckley, and I refer you to his work for more information.
Beckley was succeeded by F.E. Williamson, then the president of the parent New York Central System on May 10, 1933. Mr. Williamson was succeeded in September 1944 by H.T. Malcolmson. Malcolmson had been the General Manager of the TH&B in Hamilton, and was the first native Hamiltonian to hold a top executive position with the railway.
After Malcolmson's death in 1950, the position of President was merged with the position of President of the majority owner, New York Central. The minority owner, the Canadian Pacific Railway, was represented by their President holding a Vice Presidency with the TH&B.