The first stanza of "Elegy Written in a Country Churchyard" describes a scene near the end of the day, signifying sunset and the "solemn stillness" of night and with the subsequent stanzas, an association with death.
In lines 93-116, the speaker addresses himself and wonders how others (a kindred spirit/swain) will pass his own (the speaker's) grave and inquire about his life. The speaker imagines that the swain will recount seeing Gray (speaker) very early in the morning; perhaps with the indication that the speaker had been there all night. The speaker then imagines the swain would recall seeing him at noon watching the brook. Note that the swain's description of most vitality occurs at sunrise:
Oft we have seen him at the peep of dawn
Brushing with hasty steps the dews away
To meet the sun upon the upland lawn. (98-100)
At the beginning of the poem, contemplating life of the dead, the speaker walks through the cemetery at dusk. But when he contemplates the swain remembering his (the speaker's) own life, his wanderings are during the day. And his most energetic ("hasty steps" "to meet the sun") action is associated with the sunrise.
Life is equated with dawn and death with dusk. However, this is an oversimplification because both dawn and dusk are parts of the overall contemplation of life and death in terms of time. In his epitaph, the speaker wishes to be remembered for such a generous contemplation. Just as he remembers the poor as well as the rich, he asks others to remember him for remembering others. "He gave to Misery all he had, a tear," (123). Still, the speaker imagines the swain remembering him during the early part of the day.