This was the product of William Jay Barker. He originally sold it under the name Barker's Chevoux Tonique, starting in 1847. I found the brand name Hirsutus advertised as early as 1869 and as late as 1933.
The word "Hirsutus" and a "W.J.B." monogram (view) were registered as trademarks by Mary S. Barker in 1881. She said that the trademarks had been used by her husband from 1847 until his death in 1879.
I didn't realize until doing this article that the labels are exactly the same on the pint size as they are on the 7 ounce rectangular one. (View front label) (View side label