The speaker once told Ghaul the requirements to be chosen by the Traveler, yet he never once said that some one had to be a certain species to wield the Light,
Rather his words where: "The Light lives in all things."
I believe it would be possible for an Eliksni to be Risen by a ghost, because Fallen can be good,
many worked along side the Awoken under the rule of Mara Sov for years. Not to mention Mithrax and his newly formed House of Light.
I wish we could have Elinski Gaurdians added as an extra class, I say class because the difference in design could allow for passives or abilities designed around their extra arms that would make the race different enough to need different treatment than the others.
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The Traveler specifically gifted the Light to Humanity (and by extension the Exos and Awoken). No other species has been given this gift because the Traveler never stayed to fight the Darkness with any other species.