Ah, so this goes more into the nuance of what exactly determines the time of the circadian clock. It is very well documented that animals in the arctic circle still have circadian clocks even if it's perpetual light or dark. I left out for simplicity that the level of light matters - that is to say, if there's a time where it's slightly dimmer and a time that's slightly brighter, that is enough to adjust the circadian clock to the correct time. The adjustment process will be slower and weaker than usual, but it does happen.
Also, I hinted that animals do take in multiple measurements to determine the correct time, and that plays a role in this case. In general, light tends to be the measurement that animals will default to, but where light variation doesn't exist, animals can and do utilize other measurements to determine the time. Eating (among other things) turns out to be a relatively strong signal, so circadian rhythms end up being somewhat self-reinforcing. After all, I would expect that you only eat when you're awake.
But in general, circadian rhythms and the ways that animals adjust their rhythms to the correct time is a huge rabbithole