It took a while, but was able to run down quite a bit of obscure info on the Horse Liniment post.
First reference I found to Williams was July 5, 1875. However, it was not in association with his National Horse Medicine; rather it was HHH Horse Medicine. He was partnered up with a Mr. Moore in Stockton.
The first reference to National appeared on May 5, 1883.
Williams had apparently split from Moore and gone out on his own. Note the "remarkable" similarity between the bottles that contained the "magic elixir"~
Later, a redesigned ad with fancy graphics appeared; first date was March 8,1884.
By March 16, 1886, the ad had changed and the product was now being peddled by a drug wholesaler.
The last reference I found to the product was Nov. 20, 1886
Meanwhile, HHH continued to be sold for several more years throughout the Central Valley and SO. Cal..