Fannie may have died as early as 1879 when her daughter was born, but it looks like Thomas lived on after that if this is the right guy. Check out the 1900 census - Thomas E Sinks, a widower, is living as a roomer in Cinncinati with a Charles & Mellie King. In 1910 Thomas E Sinks is living in Detroit, MI with his son Frank W sinks and his wife Ona and her brother. In 1920 Thomas E Sinks is still in Michigan living with son Frank in Livonia, Wayne Michigan. This Thomas was born in 1848 - the same age as the Thomas born to Edward & sarah Sinks.
This may be your Thomas - can't find him in 1880 though.