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It's funny you say candle, because there were actually fire clocks that were very accurate. They couldn't tell you what time it was, but they could tell you very accurately how long they had been burning. If lit before nightfall and timed with a sundial, they were capable of rather precisely telling what time it was at night.
Similarly, sand clocks have been a thing for thousands of years. Think hourglass, but with different size holes and made of different materials with larger volumes.
They're post is almost completely backwards. Early alarm clocks were nails put into the side of predictably burning candles, that would fall out when it burned down to a certain point, which would happen at a predictable time.
Additionally, while you could probably tell the time from the moon, that would require it actually being up that night/time and then understanding a lot of complicated things about it's motion around us to have any sort of accuracy. I bet only a few astronomers have even been able to do this. Also it would be 100% reproducible because it's not like the moon makes random movements, it's perfectly predictable.
Would it be that complicated if people knew the lunar cycle, especially since the lunar cycle is fairly static? Not everyone I'm sure but those that needed a better time would probably understand and pass that knowledge along for the night folk. Of course depends when in technology we're talking but I'd assume we humans understood those cycles pretty early for our survival, not in depth but they got the idea the lunar cycle didn't change like the seasons did and adjust as needed. I haven't read up on it so I'll be glad to hear more info.
The issue with using the lunar cycle for timekeeping at night is that the moon is not always visible in the sky at night. It is also not at the same spot in the sky every night, so the math on describing the time based on moon position is actually pretty complex, and unreliable for a consistent overnight clock. You might think that tides could be used as well, but it that is even more complex. In fact, some of the first analog computers were created to do the calculus required to solve the question of timing and tides.
We think sand clocks have only been in use since the middle ages, and the reason they were invented is pretty interesting. (At least in Europe; I've looked into this before and couldn't find any other sources, but I may just not have looked hard enough).
For reasonably accurate time keeping, people had been using water clocks since at least the 16th century BCE. Basically the same idea as a sand clock, but water, which was slightly easier to feed into a reservoir. We don't think sand clocks really saw any use until the 13th or 14th century CE. Mostly, people needed to keep more accurate time on ships as oceanic voyages became more common, but the movement of the vessel messed up a water clock too badly to be useful, and pendulums had the same problem. So, enter a sand clock! Basically the same idea as a water clock, but way less prone to errors from the ship's movement.
(edit: some spelling)
Ooo, you touched on one of my favorite clock history tidbits, Maritime timekeeping. It is so fascinating. Like, the only reason spring-driven rotational oscillation mechanisms were invented was for maritime clocks. They were needed for accurate longitudinal calculations and really enabled the whole golden age of sailing. (yes, I am leaving out the Peloponnesian peoples, but they are a super awesome topic for another post)