All mentions, that I am aware of, regarding Bladesingers are below:
Bladesingers are mentioned in the edition after AD&D 2nd Edition, and despite its contradiction to 'guilds' or 'schools' there is no mention of any particular weapon (besides blades) to be in use.
What that means, in that edition, is a school representing animals went to the way side. in the revised edition, D&D 3.5 Edition, Bladesingers were mentioned as well.
It is essentially a copy paste, with a lot omitted, from Races of Faerun. Only "swordplay" and "any martial weapon" is mentioned. Nothing about schools guilds at all. There is another book the Bladesinger is mentioned, but its essentially only a blurb.
Once again, only sword is mentioned; probably due to racial sword proficiency - and the implication of blade in the name Bladesinger. Eventually, near the end of this edition, Bladesingers became Duskblades, and lost its 'elf-only' motif.
No mention of guilds or schools, or even preferred weapons were mentioned. Any martial weapon it appeared to be - but spending a feat to use a whip...most people would say, "no thank you." Bladesingers were included in the edition after this one, much to my surprise. But, it discredits the 'different weapons' aspect entirely.
Now we come to D&D 5th Edition, and you already have the published information on them thus far. Since, to my knowledge, that edition is to harken back to the days of simpler game-play and more intrinsic role-play; rather than the vice versa, take this opportunity to "Create Your Own" schools, guilds, and organizations.
There's one effect/ability that does this, but you've got to be a sprite... or get one!
(All thanks to @DrunkCynic, who put two and two together.)
In all of the core set and the Encounters supplements I can only find one thing that gets you a sort of divination of alignment: the sprite's Heart Sight ability:
The sprite touches a creature and knows the
creature's current emotional state. If the target fails a DC 10
Charisma saving throw, the sprite also knows the creature's
alignment. (MM, p.283)
As a third-level Warlock you can gain the Pact of the Chain boon and take a sprite as your familiar: "when you cast [Find Familiar] you can choose... [a] sprite. (PHB p.107)" And now you're just a touch and a telepathic back-and-forth away from knowing one's alignment.
Spells
There's nothing like the old Know Alignment of my youth. But you can Commune and pester your deity for the information.
Alternatively, you've got Glyph of Warding which can trigger on the alignment. (But process of elimination is slow.) Or you might be able to make a case to a GM that Detect Thoughts plus some skill at interpreting those thoughts might get you to alignment, but we're venturing past RAW, here. (Other spells in the ballpark are even more-problematic to try to apply with any surety.)
Magical Items
There are a few magical items that could be used in a process of elimination, as they will harm one of the wrong alignment. These items are: the Talismans of Pure Good/Ultimate Evil and the Books of Exalted Deeds/Vile Darkness. (The Obsidian Steed has a small probability of also achieving this.)
Many items can only be attuned by one of the proper alignment, but I can't think of a way to force another's attempt to attune. If you could, though, we've got a clear winner: the Eye or Hand of Vecna, either of which will change the user's alignment to NE.
[Over]Kill
A coworker reminded me at lunch of the one I'd missed: kill the target, and follow its soul to its eventual destination. Not very practical, but neither are any of the magical items....
For your reference, an Angry GM article on how vestigal alignment has become in 5e. However, he does have some constructive ideas on how to make alignment more relevant, too. (Be warned: Angry GM's materials are liberally... flavored with rude and vulgar language.)
Best Answer
There is no official lore
You can see from this tweet exchange by Chris Perkins, the Lead Designer for CoS:
As there is intentionally no information on the where the third seed is or what happened to it, it is up to the DM to decide what happened to the third seed, as he confirms in this followup tweet: