The T stands for Theodore Ebeling. A German, he was listed in the 1880 census records but not in the 1870 records so he most likely immigrated to the U.S. sometime in the 1870’s.
He was listed in various NYC Directories between 1875 and and 1892 with the occupation “drugs.” He was located in the Bronx, on Third Avenue between 146th Street and 147th Street for the entire time. The earlier directories listed his address as Third Avenue, near 146th Street while the later ones listed it as 2774 Third Avenue (essentially the same location). The 1880 census records also listed his residence at this location, so it looks like he operated a small business out of his home or lived in an apartment above the shop.
He was still listed in the 1895 Medical, Pharmaceutical and Dental Register at 2774 Third Avenue but by 1896, he had moved to 143rd Street and was no longer listed with an occupation, apparently retired.
The bottle I found is a small (approximately 4 oz) medicine with a tooled finish. It has the 2774 Third Avenue address embossed on it and also includes a logo with Ebeling’s initials T.H. Embossing on the base indicates the bottle was made by the Whitehall Tatum Company (W.T. & Co.). The fact that there’s an ampersand (between the T and Co) indicates it was made before that company incorporated in 1901. This is in agreement with an end date for the business of 1896.