I know there's a decent amount of science that goes into creating a device that can set and maintain time, so this may be a very simple question with "no" being the answer, but I'm just curious whether there is any very early history of the pendulum or other automatic timekeeping devices being used for musical purposes (accurately setting and maintaining tempo [bpm] and pulse).
One consideration is: Asking "What did people use to keep the musical pulse steady before the technology was available" might be an anachronistic angle. Richard Taruskin talks about an "evolutionary fallacy" when dealing with history—the assumption, that if we wound up in a certain situation, that prior periods somehow anticipated and aspired to that situation, and were just doing their best to figure out how to get there.
Full disclosure, I haven't actually read Alexander Bonus's thesis or chapter in the Oxford handbook about time in music. But my impression from hearing him describe it is that part of his point is that people didn't place such an emphasis on "metronomic" regularity before the metronome. It wasn't that the aesthetic desire was present and the technology was lacking; rather, the value we currently place on mechanical precision came about alongside the machine age and a growing interest in automata and measurement. In earlier periods there might not have been such an emphasis on maintaining the same tempo throughout a piece, or nailing down the exact tempo to within 5 bpm and arguing over which tempo is correct.
That's not really a direct answer to your question, but it is a part of the answer!
It is a simple question and the answer is yes. Thomas Mace suggested using a pendulum for specifying pulse in late 17th century. An early attempt at a timekeeping device was made by Abbas ibn Firnas in 9th century. But actual attempts to get the concept popular starting around 1800. The actual metronome was invented by Winkel, who realized that adding (moveable) weights at the ends of a (twosided) pendulum removes the need for incredibly long strings for slow tempi. Mälzel then added a scale, coined the term Metronome and patented it (he later lost a case). He then spent lots of effort to make the device popular.
When music is played for dancing, usually the musicians have a pretty good sense of the tempo the dancers will want. The optimum dancing tempo depends on the nature of the dance movements and the physical characteristics of the limbs and muscles. Dancing and music have gone together since ancient times; listening to music without dancing was more the exception than the rule. (I think it was in "This Is Your Brain on Music" by Daniel Levitin where I read that.) I don't think there was a way of numerically measuring the tempo, but I would guess the musicians had terms corresponding to "Sarabande Tempo" or "Tarantella Tempo" for their favorite dances.
Thousands of years ago, pendulums weren't used, but I might consider the dancers an "automatic timekeeping device," particularly if one yells out "Too slow! Play it faster!"
The first observation that a pendulum was consistent in its rate was by Galileo in 1588. It wasn't until 1656 that a pendulum was used to control a clock. It wasn't until ~1700 that someone thought to regulate music this way with numbers!! Anyway, my real answer, as a musician (http://johnsankey.ca/harpsichord.html) is that the dynamic of the human body was used, and still is. Use your arm to conduct music: each rate has a different feel to it, and with practice you can keep a remarkably uniform rate by dynamic feel alone. Any string player will tell you that their bow arm can tell them the same thing. There were lots of Italian words used to describe tempi, but the earliest texts all described how the music was to feel physically. When a conductor asks me the tempo for a harpsichord concerto, I wave my arm up and down with the feel that matches the desired tempo; no way I use numbers! Ballet performers use exactly the same thing, physical feel, to communicate tempo.