What connection does the speaker have to the neighbor at this moment? How does the speaker feel when the neighbor give up on calling the cat?

The connection between the speaker and the neighbor is emotional.

The speaker also felt lonely or left out just like the neighbour.

Explanation:

At Dusk is a poem written by Natasha Trethewey. The poem is about making own choices independent of owner's or parents.

In the poem, the speaker hears her neighbour calling out to someone. At first, the speaker though the neighbour is calling the child but she was calling her pet, a cat. The cat was playing outside in the yard and after hearing the call of its owner becomes uncertain whether it should choose to stay in the yard with fireflies or go back to the owner. The cat decides to stay and play with the fireflies.

The connection at this moment the speaker feels with the neighbour is emotional. The speaker was able to connect with the neighbour of what it feels like to wait for someone. In the lines when the neighbour gave up calling the cat, the tone becomes reflective. The speaker began to reflect upon what the neighbour must be doing now and how lonely she will be feeling. So, the connection is emotional.

The speaker feels lonely too and began reflecting if she also has someone out there to whom she can call back to home. The feeling at this moment when the neighbour has given up on calling the cat is lonely and melancholy. The speaker, here, begins to share her own feeling about the melancholy experience of waiting for someone to come back home.

When one call out someone and there's no response, one feels lonely and that's what the speaker is feeling; the pain of loneliness of the neighbour.