Are those clocks based on actual time or something else like reactions to lighting or number of heartbeats (which probably averages out to the same amount per day)?

There is a base circadian period which is roughly the length of a day, but it varies between individuals. If you put people in caves with no light at all, they'll still naturally fall into a sleep/wake cycle around 24 hours (it tends to be slightly longer).

Specifically it comes from your SCN https://en.m.wikipedia.org/wiki/Suprachiasmatic_nucleus

The answer is it's evolved and some kind of complex cellular feedback mechanism, but Wikipedia is a bit light on details. Apparently this clock is also fanned out in some way to other parts of the brain/body which also follow a daily cycle.

https://www.sciencedirect.com/science/article/pii/B978044459...

https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2735866/

Light isn't mandatory, but the SCN will synchronise to daily light patterns (eg when you travel). The SCN is also physically located close to the optic nerve. I think this is why the underlying rhythm is a slightly longer than a day, because it allows the body to reset it to 24 hours. If the period was shorter, even slightly less than 24 hours, maybe you'd have problems when the clock restarted before the day finished and the error would propagate over time (you'd keep shifting the cycle).

Measuring regular changes in lighting (the day/night cycle) is actual time. (So would be heartbeats, although heartrates vary so much that measuring them would be very inaccurate on a daily scale.)

All definitions and measurements of time rely on counting events that are believed to happen at regular intervals. A second was defined for most of history as 1/246060 of a solar day, in other words, measuring changes in lighting.

I agree but I don't know if that explains how humans can tell time. If you put a human in a completely isolated room with no lighting changes then I doubt they'd be able to count the number of days.

Humans can't tell time accurately without external cues about the day and night cycle. We also can't tell time accurately to the minute if we can see outside but don't know how long the day is, i.e. latitude and time of year.

We can tell time inaccurately by timing somewhat regular internal biological events. That pretty much follows from the definition of time as the interval between regular events (which are assumed for physical reasons to be equally spaced). The only question is which underlying events we use and how.

https://en.wikipedia.org/wiki/Time_perception

I think the base circadian day time is about 25 hours, or 24 hours 11 minutes, or similar [1].

I've always wondered what would happen to the sleep cycles of astronauts on long space journeys. They may not have "daylight" to regulate their rhythms.

[1] https://news.harvard.edu/gazette/story/1999/07/human-biologi...

You don't need to go on space journeys to observe people's rhythm shift.

https://www.ncbi.nlm.nih.gov/pmc/articles/PMC1330995/

It's supposedly regulated by light and by magnetic fields: https://www.nature.com/articles/458948f