Biological clocks for cave dwellers are driven by hunger
In experiments on Somali Cavefish, which have been isolated from sunlight for million of years, the fish were found to be unresponsive to artificially imposed dark light cycles, but that their circadian rhythm could be modified by feeding them at certain time intervals during the day.
Other variables that can control circadian rhythms include temperature changes and social interaction. Most fish species in rest-activity cycle studies maintain a near-24 hour circadian rhythm; this is probably due to having been derived from a surface-dwelling fish and having no reason to change the activity cycle. However, one species in the last linked study changed their rhythm to 38 hours. The authors do not propose any specific reason for the change to a 38-hour schedule, but it is possible that it was driven by the food availability or social interaction mentioned in the previous studies.
Lastly, in the last linked study, the cave dwelling species that maintained a 24 hours cycle usually slept much less than their surface dwelling counterparts. Surface fish slept in 2-3 hour bouts for a total of 12+ hours. The cave fish slept for many 15 min or less segments for a total of only 2-3 hours.
A cave dwelling civilization organizes around communal feasts
For a species of cave dwellers with absolutely no contact with the surface and the sun, a likely result would be organize a time schedule around communal meals, ticking off both the hunger and social activity blocks for maintaining schedules. These schedules could be 24 hours, or any other time unit, apparently.
These creatures would probably not sleep continuously through a 'night' but would catnap throughout the day. Every 4 to 6 hours, perhaps, there would be a community meal, where everyone gets together and eats. For a stone-age level people, this meal would be regulated by the genetic circadian rhythm of each individual; the social interaction provide a means for calibrating the internal clock with the other members of the tribe. As technology advances, water-clocks or hour-glasses would begin to be used to help time the meals more precisely, until eventually mechanical clocks are invented.