If it doesn't need to be mentioned in the movie, why does it need to be mentioned in the RPG? And if it doesn't need to be mentioned in the RPG, why should it matter.
I play some RPGs which require tracking of time by the day, and sometimes more fine-grained than that - eg Classic Traveller.
I play others that don't require tracking time at all - eg Marvel Heroic/Cortex+.
As far as contemporary D&D play is concerned, I think keeping track of time spent between rests probably matters (for spell durations and the like), and noting when a rest occurs matters, but beyond that the passage of time seems like mere colour.