Here's a different approach to answering your question. Another completely valid, and backwards way of asking your question would be to ask: "How did people know that a hydrometer was an indicator of the beer being done?" The hydrometer really doesn't tell you that your beer is "done". What it tells you is that the sugars have been converted by yeast into alcohol and CO2 (among other by-products). I certainly wouldn't consider a Russian Imperial Stout or Barley Wine done the moment the krausen dissipates back into the beer and the hydrometer hits its FG. Each beer is different, just how every brewer is different. Their interpretations of "done" are all subjective, influenced by others imparting advice and education on them and previous attempts.
There is no right or wrong way to brew a beer (probably the most over-stated piece of advice, second only to Papazian's "Relax, don't worry, have a homebrew", bear with me here). By that logic, there is no wrong way to call a beer done. Each brewer has their own idea of when their beer is ready to serve, they don't need a hydrometer each time to tell themselves that. Heck, I didn't bother to take final gravity readings on two of the five beers in my keezer. They tasted great, I was excited to get them carbed up, and to this day, I don't know what the exact ABV of them are, but I'm confident they're done. My measure of "done" is that it tastes how I wanted it to taste, if not better. I bet brewers back hundreds of years ago used the same methods to determine whether or not their beer was done.
Probably not the most factual answer you would hope for, but hopefully it allows you to take a broader approach to understanding how it worked back in the day.