"It is said that the towers of Emyn Beraid were raised by Gil-galad for Elendil, his friend; and the Seeing Stone of Emyn Beraid was set in Elostirion, the tallest of the towers. Thither Elendil would repair, and there he would gaze out over the sundering seas, when the yearning of exile was upon him; and it is believed that thus he would at whiles see far away even the Tower of Avallone upon Eressea, where the Masterstone abode, and yet abides."
J.R.R. Tolkien - The Silmarillion, p. 352
He found him in the high tower of Elostirion, gazing westwards, inwards, his head slumped ungracefully against the smooth round orb of the Palantir, his arms resting forlornly on the marble pedestal on which the Seeing Stone was placed. His stance conveyed ultimate sadness and Gil-galad stood for a moment, not knowing whether he would proceed, or retreat and leave his friend to his innermost thoughts. The matters of state at hand were too pressing, though, so he crossed the room and put a gentle hand on Elendil's shoulder, desiring to shake the Man out of his self-inflicted misery.
"Do not hurt yourself so, my friend. I did not erect this tower to let you torment yourself. Why do you look back when the future demands your full attention? Elendil, you cannot live in the past forever: pressing matters have presented themselves, requiring your immediate attention."
Elendil did not turn around immediately, but seemed to draw at least some comfort from Gil-galad's cool strong hand resting on his shoulder. He sighed once, deeply, gathering his composure, and then turned around to face his friend.
"It is not the sad satisfaction of gazing into the past that I seek, Gil-galad, my friend of old. I look to the West to see if any help may come from there to aid us in our battle. Long has it been since I looked towards Atalante in the vain hope of seeing her green clad burial mound rise up from the waters in which my homeland has sunk for good. You know full well that I only took the memory of her with me when I fled from the downfall of Númenor with Isildur and Anarion, and was finally cast ashore on your land, a bedraggled victim of the waves, with just a few heirlooms to prove my Númenórean inheritance to you. What saddens me most is that I have not seen nor heard from my sons since more days than I can remember, and I fear that the worst has happened to them."
Gil-galad knew that Elendil spoke the truth and that Almandire was no longer a part from the Man's life, save as being his beloved long departed wife and the mother to his lost sons, and even though he grieved for Elendil's loss it also filled his heart with tentative joy. For Gil-galad had loved the fair Man of Númenor since he found him cast ashore with his ships broken by the waves, their sails ripped by the wind, the last remnants of a kingdom lost forever. He knew it was not the way of the Númenórean Men to take other men as their lovers, but hope springs eternal, and he had never given up the hope that one day Elendil would see that wisdom could lie in other ways as well. For friendship could take as many forms as there where friends. Gil-galad had not taken a wife as Elendil had done, but he was well versed in the ways of lovemaking, and he had discovered early on that the love of women was not his way.
But those thoughts were far beyond him now, for as he had told Elendil, pressing matters were at hand: Elendil's son, Isildur, having built the Kingdom of Gondor with his brother Anarion in the south, had arrived with his family and a scattered few of his followers to petition the help of his father and any other alliance he might provide. Sauron, their terrible foe, had cast the lands of Gondor into darkness and Isildur had barely been able to escape to the North and search for help while the rest of their people were scattered, hiding and huddling pitiably in dense forests and caves filled with dread.
"Elendil, your son, Isildur, has arrived, his family nearly drowned, he himself all but collapsing with fatigue to ask for your help. It seems that you should cease looking Westwards, longing for help; your gaze should turn Eastward now and you should be the one providing succour to your nearly defeated people."
"Isildur has fled to us, you say?" Elendil said as he clasped Gil-galad's hand on his shoulder, gripping it and urgency mingled with gladness at the news his friend brought him, lifting his fallen mood.
"Come, Gil-galad, lead me to him for I have not seen him in many a year," he said as he moved past Gil-galad, the Elven-king's hand sliding off the Man's shoulder as he did so. "I, nay, /we/ must speak to him and hear of Sauron's great misdeeds and perhaps of Anarion's fate, and then plan our attack."
"My friend, go to Isildur and speak with him," Gil-galad answered, "for it has indeed been a long while since you two met and his plight has been great. I will join you shortly and we will discuss our strategy to defeat Sauron. For this is what we must set out to do."
Elendil left then, casting one final glance towards the Elven-king before he did so, but Gil-galad did not follow him down the long, winding stairs of Elostirion. Instead, he turned toward the window that faced Westwards and watched the sun set there, blood-red and menacing, while roiling black clouds started to gather in the East.
According to the index to the Silmarillion, Gil-galad means 'Star of Radiance'. Elendil can be translated either by 'Elf-friend' or 'Star-lover'. I'm probably reading more into this little fact than I should, but then again, Tolkien does not give names without reason. :-)