The "tremulous," or tremblingly fragile "stay" on earth is, like many of the images in the poem, unexpected. Why can't he just call it his "life," since that's what he means? Calling his life his "tremulous stay" calls attention to the uncertainty of life (it is "tremulous") and to the passage of time; it's a "stay," or a visit, of a certain period.
[…] like an eyelid's soundless blink (5)
This simile describes the silent flight of the "dewfall-hawk," but the "blink" of the "eyelid" also sounds like the way we describe something that happens quickly – something that goes by "in the blink of an eye." This could be a way for the speaker to imply that life is brief, and goes by "like an eyelid's soundless blink."
If, when hearing that I have been stilled at last, they stand at the door (13)
The word "stilled" as a euphemism for death implies that the speaker's forward progress has been frozen. But even the news that the speaker has "been stilled" is enough to freeze the neighbors, too. They "stand at the door," as if uncertain whether to go in or out.
And will any say when my bell of quittance is heard in the gloom, (17)
Here, the speaker does away with any "if" statement – he knows that his "bell of quittance" will someday be heard. So he doesn't bother with "If my bell of quittance is heard." Death is unavoidable, so the bell marking his death is, too.
And a crossing breeze cuts a pause in its out-rollings, (18)
Death, and the accompanying funeral bells, might be unavoidable, but somehow nature is able to interrupt it. The "crossing breeze" is able to "cut a pause," or interrupt the sound of the bell. It's as though the breeze were able to disrupt the flow of time itself.
Till they rise again, as they were a new bell's boom (19)
Of course, the "breeze" can't stop the flow of time forever – the sound of the bells picks up again when the breeze dies down. But the words "rise again" suggest the possibility of life after death by alluding to the Christian idea of physical resurrection on Judgment Day, and the alliteration of the "new bell's boom" draws our attention to the "newness" of the bells, which suggest the possibility of renewal. At least the poem doesn't end on a totally depressing note.