Let's look at the actual requirements of a long rest...
A long rest is a period of extended downtime, at least 8
hours long, during which a character sleeps or performs
light activity: reading, talking, eating, or standing watch
for no more than 2 hours. If the rest is interrupted by a
period of strenuous activity-at least 1 hour of walking,
fighting, casting spells, or similar adventuring activitythe
characters must begin the rest again to gain any
benefit from it. (PHB, 186)
Trance. Elves don't need to sleep. Instead, they
meditate deeply, remaining semiconscious, for 4
hours a day. (The Common word for such meditation
is "trance.") While meditating, you can dream after a
fashion; such dreams are actually mental exercises that
have become reflexive through years of practice. Afler
resting it this way, you gain the same benefit that a
human does from 8 hours of sleep. (PHB, 23.)
Noting that trance allows dreaming... during the 4 hours of trance, it's fair to say that they are pretty far out of it. If the sleepers get a roll to wake, the elf probably should get advantage on that roll, but still should need to roll.
During the other 4 hours, they're awake. Note that other races only need 6 hours of sleep, but 8 hours of rest.
And standing watch is explicitly allowed as a resting activity.