I fast and maintain a ketogenic diet. Its 5:45am as Im typing this. Ive been up since 4. Went to bed at 11. Currently on hour 35 of a fast that I plan to end mid morning. Unless I still feel "great"...
I have high mental clarity currently. I had high mental clarity when I went to sleep. I did have issues sleeping, but this is nothing new on a ketogenic and fasting state.
From the vast research I've done, sleeping may be more important on a high-insulin-fluctuating diet. However, when the body and brain are fat adapted (less insulin), there is a constant fuel source. The brain operates very efficiently on ketones. Also, important to note that when fasting and doing keto, you must supplement electrolytes.
There is a lot more to all of this and the notion behind the importance of sleep. Anecdotally, diet proves to be more important for me. Do your own research.