The Mark

I spent about 20 minutes trying to figure out what to do here.

Get in position (in the center of the rune), and it will glow. Then you target Eyir (you need to do this), and finally, /kneel.
Then you'll get credit.

Introduction
This quest is part of a comment-size guide for "Balance of Power." questline. Quests are pretty much self-explanatory and all it takes is some time and good will to complete them. Completing this questline rewards Artifact Appearance (Appearance 3, Tint 1).

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Part 1
Image of Kalec appears in your Order Hall and gives you the following quest:
The Power Within (Meet Archmage Kalec at Azurewing Repose in Azsuna.)
Reasons behind appearance of Archmage Kalec in your Class Order Hall are not yet completely understood but most people noticed him few days after they completed their Class Campaign.

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Part 2
From there you take a next quest from Senegos:
The Heart of Zin-Azshari (Retrieve the Heart of Zin-Azshari and defeat the Wrath of Azshara in the Eye of Azshara on Mythic difficulty.)

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Part 3
After completing the previous quests you receive a few new quests (exactly 3: two from Senegos and one from Archmage Kalec).
Senegos:
[1] A Vainglorious Past (Obtain a Vainglorious Draught from Veridis Fallon.)
- You can purchase Vainglorious Draught from Veridis Fallon in Crumbled Palace [46.9 , 41.4] in Azsuna for 150g (Requirement: Court of Farondis - Honored).

[2] Fallen Power (Recover a Corrupted Essence from Oakheart and defeat the Shade of Xavius in Darkheart Thicket on Mythic difficulty.)

Archmage Kalec:
[3] Tempering Darkness (Obtain 30 Blood of Sargeras.)
Should not be a problem since by the time you get that quest and if you did not spend any Blood of Sargeras you should have some stacked up simply by completing Dungeons and World Quests.

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Part 4
Archmage Kalec:
Lucid Strength (Absorb the power from the Corrupted Essence using the Heart of Zin-Azshari.)
Right next to you.

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Part 5
Senegos:
The Wisdom of Patience (Await the opening of The Emerald Nightmare, then report back to Senegos in Azsuna.)

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Part 6
Archmage Kalec:
[1] In Nightmares (Obtain a Deathglare Iris and the Horn of the Nightmare Lord from The Emerald Nightmare.) NOTE: NOT doable with LFR. It has to be Normal difficulty or higher. In order to complete this quest you need to kill 2 bosses: Il'gynoth and Xavius and loot mentioned quest items.

Senegos:
[2] Essence of Power (Collect 30 Corrupted Essence from The Emerald Nightmare.) This quest gave me a weird WoD and Khadgar flashback. NOT doable with LFR. Only Normal or higher difficulty. Essences do not have a 100% drop rate and bosses can drop 1-2 3 Corrupted Essences at the time.

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Part 7
Senegos:
Essential Consumption (Absorb the combined power of the Corrupted Essences using the Heart of Zin-Azshari.)
Right next to you.

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Part 8
Archmage Kalec:
Repaid Debt (Meet Archmage Kalec in the Shal'Aran in Suramar.)

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Part 9
Thalrenus Rivertree:
Lost Knowledge (Obtain the Scroll of Elun'dris from First Arcanist Thalyssra.)
- Costs 120g. Requirement: The Nightfallen - Revered).

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Part 10
Thalrenus Rivertree:
[1] Borrowing Without Asking (Recover a Containment Crystal from the Vault of the Wardens on Mythic difficulty.)

Syrana Starweaver:
[2] Rite of the Captain (Take Advisor Vandros' Eon Winder from The Arcway on Mythic difficulty.)

Lothrius Mooncaller:
[3] Literary Perfection (Find Lothrius' first edition copy of "Wards, Sigils, and the Nightborne Way" in the Court of Stars on Mythic difficulty.)

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Part 11
Syrana Starweaver:
Twisted Power (Use a Greater Portal Stone to summon Vizuul the Twisted at the Altar of End Times in Faronaar and collect his runebindings.)

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Part 12
Syrana Starweaver:
A True Test (Absorb the power from the Twisted Runebindings using the Heart of Zin-Azshari.)
Right next to you.

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Part 13
Archmage Kalec:
Seeking the Valkyra (Seek out Ashildir at the Vault of Eyir in Stormheim.)

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Part 14
Ashildir:
The Mark (Prove your worth to the Valarjar, then receive the Mark of the Valkyra from Eyir.)

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Part 15
Ashildir:
Retrieving the Svalnguard (Retrieve the Svalnguard and defeat Helya in the Maw of Souls on Mythic difficulty.)

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Part 16
Ashildir:
[1] A Feast Fit for Odyn (Acquire flank meat from Thunderhoof in Stormheim, Spinesever's spine in Highmountain, and a steak from Leytusk in Azsuna.)

[2] Presentation is Key (Retrieve 4 Adamantium Casing Scraps and defeat Dargrul the Underking in Neltharion's Lair on Mythic difficulty.)

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Part 17
Ashildir:
Odyn's Blessing (Obtain Odyn's blessing in the Halls of Valor on Heroic or Mythic difficulty.)
- Use Grand Feast of Valhallas when you enter the dungeon - at the start. You can enter the dungeon alone, put the feast down, get out and then get a group to defeat Odyn and get his blessing. After you defeat him wait for him to finish his speech (RP) and then you can collect his blessing on the loot chest.

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Part 18
Archmage Kalec:
Planning the Assault (Await the opening of the Nighthold, then meet Archmage Kalec in Shal'Aran.)

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Part 19
Archmage Kalec:
[1] Into the Nighthold (Collect 20 Nightshards from the Nighthold on Normal difficulty or higher.)
- Try and complete this quest without killing Gul'dan because if you kill him before acquiring The Nighthold: Darkness Calls quest in Part 20 he won't drop quest item for you this week and you'll need to wait for a next reset to complete The Nighthold: Darkness Calls quest in Part 20.

Thalrenus Rivertree:
[2] The Nighthold: Delusions of Grandeur (Collect the core of Trilliax and Grand Magistrix Elisande's Millennia Tome in the Nighthold on Normal difficulty or higher.)

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Part 20
Archmage Kalec:
The Nighthold: Darkness Calls (Bring one Gul'dan's eyes to Archmage Kalec on Normal difficulty or higher.)

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Part 21
Archmage Kalec:
Balance of Power (Absorb the combined power of the Nightshards and the Eye of Gul'dan using the Heart of Zin-Azshari at the Lunar Crucible.)

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Congratulations on completing this questline and acquiring new Artifact Appearance. Enjoy!
Foxies, out.

You have to target Eyir and /kneel. If you don't, it won't trigger the dialog.