Nobody knew nor cared how many pulses there were in an hour. But a person’s pulse was still used as a short unit of time.
I’ve never heard of the pulse being used to measure time. Do you have any cites?
For one, that’s how Galileo first noticed the constant timing of a pendulum.
But we’re talking about the ancient world.
We were shown a way of getting remarkable precision for an estimate of the speed at sound at school. Find a large surface that you can get an echo from. We used the side of a school classroom block. Stand back from it a hundred meters or so. Measure exact distance. Slap together a pair of bits of wood. The echo comes back. Now start slapping them together at a rate that puts your slap in the middle of the return. Get into a steady rhythm. Start a stop watch and measure for say a minute whilst counting slaps. Speed of sound is round trip distance multiplied by the number of slaps divided by the measurement time. You can get two significant figures.
Not a method available to ancient civilizations.
Well the precision one needs to measure a value to is intrinsically limited to the precision you are able to measure. In principle you could sit there banging away at the wooden blocks for an hour as measured by a sundial. Or perhaps a water clock. Prior to a pendulum clock a pulse rate sufficed. If you counted 60 heartbeats you would get a pretty good measure of the speed of sound referenced to an average heartbeat.
Or the time it takes you to sing one verse of a song. Or find the right distance so your clapping matches the tempo of the song.
I recall reading an article in Scientific American many years ago which argued that while Galileo claimed he timed the pendulum by his pulse, it’s more likely he used the tempo of a song to do it. Singing at a consisent tempo is pretty easy for humans and is (according to the article) more accurate than pulse timing. By this argument, Galileo claimed he used his pulse rather than singing because it sounds more scientific. I haven’t been able to find references to this theory; searches involving “Galileo” and “song/singing” mostly turn up references to Bohemian Rhapsody.
Or the guy with a drum on a slave galley.
The Sound of Music is in the hills. Just like the Sound of Silence is in tenements.
Cite? 
I was there.
I don’t think it has been mentioned yet how ancients realized that light travelled much more quickly than sound.
They realized that people often appear intelligent until they open their mouths! 
What I had heard was that the initial observation of the swinging lamp was using his pulse, but that his later experiments with rolling objects down ramps (not freefall-- It’s easier to time things on ramps, because they’re slower) were probably done with a song.