Supposedly, your dwarves are still biological creatures, so they will have some natural circadian rhythm. Even without the sun, they would like to sleep for some time and eat several times a day. Most likely, their rhythms will be even more robust and less dependent on the artificial lightning then humans. The research says that even creatures in environments where the changes in lighting doesn't affect them, such as naked mole-rats, still have cyclical patterns of activity and sleep of almost precisely 24 hours.
So, the individual dwarf would understand the basic pattern of working period vs sleeping period, and the whole settlement would control and optimize those rhythms for communal activity.
Now, for the longer cycles. Possibly, your caves are not completely isolated from the outer worlds. There may be some changes of temperature, air flow or water flow depending on the conditions outside. They will be the 'seasons' for your dwarves. Obviously, they would not be called winter or spring. But there will be a season when the glaciers on the mountain start melting and the water level in the underground lake rises. Or the season when the warm air moves in the rightmost corridor, or cold air in the leftmost.
So, there will be some perceptible changes corresponding to the seasons outside - not completely rhythmical, not present every year, but significant enough that the dwarves themselves will notice them. And if they have at least some activity that depends on year-long cycle (breeding bats or growing mushrooms, for example), they would try to keep track of those patterns.
Water clocks, daily bells, yearly festivals - all that stuff would most likely still exist in their society.
There is a problem that for them there will be no 'objective' way to check the time - they will not be able to measure it by the position of the stars. Possibly, the timekeeping in different settlements will drift off, the day shifts would start at different time, the yearly festivals would move by the couple of days.
Timekeeping could even have deep cultural significance for them, being analogous to the concepts of 'thinking', 'speaking' or 'being civilized' for humans. A civilized dwarf keeps time carefully, always gets up with the morning bell, always checks his water clock, always keeps a calendar and celebrates the festivals.