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Shouldn't this have a "Type I / Type II" distinction, for nosebleeds caused by the characters' (over)use of their own psychic powers, vs. those caused by them being under psychic attack?
Best not to do so. Type Labels Are Not Examples, after all.
I don't think it's much of a stretch to say the weird brown head-dripping from The Fifth Element is of a similar sort of phenomenon. The space devil communicating with someone seems to shock their body enough to make it drip.
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How well does it match the trope?