Brink was the Republican candidate for the office of supervisor, and garnered quite heavy support from both parties.
However, following a recount, Brink was declared the winner, and became the first Republican elected from the town of Ulster in over 20 years.
During his terms as supervisor, Brink took a financial situation in disarray within the town and helped to improve it through honest means and sensible business administration.
His experience in the mercantile business helped to shape his approach as supervisor to the town's needs and issues.
For many years, Brink served as one of the board of managers of the Ulster County Tuberculosis Hospital.
He was also a trustee of the Ulster County Savings Institution starting on July 19, 1921, and would stay in this position until January 17, 1938, when he was elected president.
Jacob's son, Joel's second cousin, Erastus Brink (1838–1902), succeeded his father as supervisor of the town of Kingston in 1877.