Ealcil is an Altmer sorcerer and researcher found initially in Eagle's Strand. He is the author of several notes, and is involved in several quests, including "Storm on the Horizon." He can be found at the Temple of the Mourning Springs after completion of the quest "Tears of the Two Moons."
Prior to the Vestige arriving on Khenarthi's Roost, a storm caused the destruction of a number of ships in the Aldmeri Dominion fleet. Ealcil was one of the people dispatched during this time, arriving at Eagle's Strand to deal with problems, as well as investigate the rumors about special waters on the island.
Joined by Gathwen and Rurelion, Ealcil embarked on an expedition into the Temple of the Mourning Springs based on the stories he heard. After arriving, the party found the source of the water: the Mourning Stone. The group was shortly attacked by undead, causing them to separate. Ealcil alone returned to Eagle's Strand with the Mourning Stone.
Ealcil is a scholar, and, as such, wishes to study the Temple of the Mourning Springs, as well as the Mourning Stone. He is amazed by the stone's ability to produce endless water, and studies it extensively, almost disregarding everything else that's happening on the island. He is described by others to focus a little too much on his study, which is why he removed the Mourning Stone from the temple without a second thought. This is apparently typical of Ealcil.
Razum-dar tells the Vestige to speak to Ealcil about recent occurrences on Khenarthi's Roost. Ealcil will mention that there have been undead problems around the Temple of the Mourning Springs. After brushing off any responsibility for the undead, he will also talk about possible survivors on Shattered Shoals.
Although he does not speak to the Vestige directly during the quest, he can be spoke to prior, after Razum-dar mentions trouble at the Temple of the Mourning Springs during "Storm on the Horizon." Ealcil will mention that he took the Mourning Stone from the temple, right before undead attacked the party. The Vestige journeys there to stop the undead that have arisen from Mourning Springs, finding Gathwen, who will officially start the quest.
He will give the Vestige Ealcil's Lodestone to deactivate the Storm Totems.