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Pretty much the opposite. I dont know the exact requirments anymore out of my head, but I can look up later when I am back on my pc.

You need to finish the dungeon while having done close to the bare minimum. Collet as less forms and reputation as possible, ignore most side quest. I think the lowest amount of flames that can be  lit and to still progress are 10. Could be that just igniting the lowest amount of flames could be already enough. If not than the reputation also need below a certain number.

I finally had the time to look it up. Sorry it took longer. So to answer fully:

 You need to lit under 20 flames and have a reputation under 500.

And you do get both skills (7th and 8th tail) once you get the kitsune form, if you play through the game with the Light & Dark Perk enabled.