I believe, with a tooled top, that 1880s would be accurate, although they were also produced far earlier than that. Here's an OP example that I found a few years ago in a well we uncovered on my property.
I also have one with the open pontil. Here is some interesting info I picked up off the internet but can't remember where. Take it with a grain of salt, but it sounds good to me:
Personally dug in San Francisco Victorian 1870'sAqua F. Brown's "Ess of Jamaica Ginger Philada" medicine bottle. Thefront body is strongly embossed vertically, "F. Brown's Ess of JamaicaGinger Philada", and measures 5 1/2" high. Essence of Jamaica Ginger,commonly known as "Jake," was sold as a medicine in the 19th centuryas a remedy for colds, menstrual cramps and digestive issues. Its high alcoholcontent made it popular drink As a result of Prohibition, producers of themedicine sought ways to mask the product’s high alcohol content by addingvarious substances, such as triorthocresyl phosphate. The compound didn’t alterthe medicine's taste, but it masked the amount of alcohol the beveragecontained. Around 1930, consumers of the drink began reporting muscle weakness,tingling and paralysis in their extremities, some sufferers forced to lifttheir leg high in the air when they walked so their paralyzed foot would clearthe ground. It was discovered that triorthocresyl phosphate was a powerfulneurotoxin that damaged the neurons that control movement, and Jamaica Gingerwas outlawed soon after. Those afflicted with permanent neurological damagecame to be known as “Jake Leg.” The social stigma associated with their conditionwas particularly harmful and often prevented them from reporting theircondition. It has been reported that sufferers were reduced to begging in thestreets.