Agreed that in that context “day or night” means there’s no respite. Agreed there’ll be no celestial objects in the eternal state to give light. (Rev. 21:23 and 22:5)
I don’t think the “Book of Life” is for God’s reference, but for ours. He’s omniscient and records everything, including any events we hope are hidden. This is a trial for the ultimate destination of our eternal souls and that’s His evidence.
The term/phrase is used too many times for me to not believe it’s an actual document, or will be perceived by us as an actual document.
An actual document we can touch and feel, though we lack form?