Heavensward Job Quest for PLD is specifically about returning the aura to Oathkeeper, and Syl-what's-his-name uses Constraint & the Warrior of Light to further this goal. In the end, the Sword will only glow for the Warrior of Light, who passes it along to what's-his-name so he can strive to make it glow for himself. The glow (ie the Oathkeeper) is actually the Soulstone and the Paladin whom carries it, not the sword itself. This is why the Sword glows for the Warrior of Light and not the others. The WoL themself is an Oathkeeper (ie a Paladin better than the rest, free or Sultansworn).