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In the last couple days, I've caught Bill snoozing on his basking rock (with the lights on) a couple times. He quickly becomes awake and alert when I make some noise and takes a dive off the rock and swims around. His appetite is excellent and he spends most of his basking time alert and awake.

Is it OK/normal for him to take an occasional cat nap during the day?

Definitely normal. Sounds like he is just relaxing

Oh good! He looks so cute doing it.