The Neighbors rustle in and out — The Doctor — drives away — (5-6)
Here's the guest list: neighbors, check, rustling. Doctor, check, driving away. These facts are stated plainly, logged for the record. It's like people who automatically take a head count at a funeral, as if that meant something. Does it?
The Minister — goes stiffly in — As if the House were His — And He owned all the Mourners — now — And little Boys — besides — (13-16)
If this is a drama performed for onlookers and attendants, then the minister is hamming it up. He strides into the house and immediately tries to steal the whole scene. Is commanding mourners under his job title? He certainly seems to think so. He acts as though he owns even the little boys in the neighborhood (though we all know that those squirrely kids are wild things).
And then the Milliner — and the Man Of the Appalling Trade — To take the measure of the House — (17-19)
It would seem that death is a cottage industry in this poem, quite literally. Everybody is in on the act. Here comes the hatmaker evidently to take measurements for funeral bonnets. And on his heels, the "Man Of the Appalling Trade," the undertaker given a nervous euphemism. His trade may be appalling and turn everyone pale, but he fulfills a very necessary role.
It's easy as a Sign — The Intuition of the News — In just a Country Town — (22-24)
After listing all of the participants by name, the speaker uses the last lines of this poem to summarize his impressions and to bring the town together. All of the people and their activities are "a Sign" and contribute to an intuition of the news of this death. The town itself has it within itself to read the signs of this death, to understand, as one. It's not only the one observer-turned-speaker now; he speaks of the whole "Country Town." Notice how Dickinson says it's just, which means "merely," but conveys a sense of justice or rightness. It's as if she's saying, how it is, is how it should be.