What does the narrator think about death in the second period of "The Pit and the Pendulum"?

My copy of “The Pit and the Pendulum” is not divided into periods, so while I cannot address that specific aspect of your question I’ll try for an overall analysis of death.

Death is obviously a major theme within the story (as it is within much of Poe’s works), and its relationship with human consciousness is emphasized in this particular instance. On an initial and obvious level, death is something to be feared:

“The sentence—the dread sentence of death—was the last of distinct accentuation which reached my ears.”

Here the narrator is so horrified by his decreed fate that at least one of his senses fails him. Yet on its own this is a reductive explanation—it is not necessarily death itself that he finds so repugnant—it is the means of death that he fears, how and when it arrives:

“The mode and the hour were all that occupied or distracted me.”

With this the narrator reveals that it is the unknown which, when added to the equation, lends the concept of death such horror. He mentions all the rumors and tales told about the creative cruelty utilized in the Inquisitorial monks’ punishments. So on a physical level, death is inconsequential. It is natural, and can even be a preferable state due to its simple finality:

“And then there stole into my fancy, like a rich musical note, the thought of what sweet rest there must be in the grave.”

On a mental/psychological level, death can be something to be feared. The narrator mentions moments where his body is physically restrained, hampered or unconscious but his mind’s activity continues. The main character is actually quite clever, a very quick and intellectual individual. This trait serves him well in that it helps him comprehend his situation and create solutions for his problems (measuring the dimensions of his cell, freeing his bonds via ratty ministrations). However, it is his abstract and overactive thinking that prolongs and emphasizes the terror he feels concerning his demise. One could even consider that it was the narrator’s active mind that landed him in the clutches of the Inquisition, an organization notorious for its tendency to kill off intellectuals and free-thinkers.

So as it pertains to the story, death is a sentence, a state, a destination, a relief, a motivator and yet at the end is avoided. Perhaps the overarching message is an irony: that something so ultimately simple and infinite can create such vast strife within ourselves and our society.