"Rhapsody on a Windy Night" is likely the best poem of Eliot's to explore the theme of time, as it is first and foremost an exploration of time, how it contributes to our experience with life, and, ultimately, the futility of how carefully we collect and spend our time.
The poem follows the speaker, who wanders around a city street from 12:00 to 4:30 in the morning. Since it begins at midnight, there is a dark inversion on the trope of midnight having an association with the supernatural. Instead of being transported to a world of fantasy, the speaker finds himself in an eerie world of decay, loss of memory, and diminishing control.
As the hours go on, memory mingles with the world that the speaker sees at midnight, he sees a (presumable) prostitute standing in a doorway with tattered clothes and cat eating spoiled butter. The decay and loss around him conjures up bizarre memories that seem drawn at random but that are indicative of the losses that he has felt throughout his life compared to the universal loss that he sees represented in the city and the conversation of the streetlights.
Finally, at 4:30 am, the speaker goes to bed to anticipate the drudgery of the next day. He says that this is the final "twist of the knife," referring to the idea that despite the constant decay, it never ends. There is no final dignified death of memory, it just fades and becomes insane slowly and eternally.