I don't normally experience the time interval between when my input streams shut down every night and reboot every morning either, though.
Nothing prevents one from running an LLM whose harness has a clock and a while loop in it, and it would be weird if its mere lack were really so consequential to consciousness.
Exactly, the clock is external to the model. Nothing prevents it from being faster or slower, or even running backwards, because it’s ultimately just another data point in the input stream to a computer function.
Your brain and your whole body exist in time. Even when you are asleep, your body does not flicker out of existence and your brain actually continues working during that time.