Not directly on Paarl, but Archibald, who was fascinated by the darkbeasts and the natural lightning they emanate. Paarl drops the Spark Hunter Badge, which says:
"Badge crafted in secret by Archibald, the infamous eccentric of the Healing Church, for his friends.
Archibald was fascinated by the blue sparks that emanate from the hides of the darkbeasts, and dedicated his life to its artificial reproduction. in a style of inquiry that, incidentally, closely followed the methodology of Byrgenwerth."
It's a secret badge Archibald gave to his closest friends, I just assume Paarl was one of those friends, and the hunter badge artifical lightning properties kept working even after Paarl went mad and became a beast himself. Which is why his lightning isn't constant, as the actual darkbeasts you fight (like the cannibal), but instead kind of a buff Paarl constantly casts on himself, and you can interrupt by staggering him.
I assumed Paarl was one of Archibald's closets friends, and, because of his lightning powers that kept working even after he became a beast, he was given the name Darkbeast Paarl.
Either that, or Paarl was never human and was actually an artificial Darkbeast invented by Archibald and locked down there, but then it wouldn't make much sense to mention "for his friends" in the badge description. Or rather, it would make sense, because the artifical reproduction part would still be important, but it shouldn't drop from Paarl, but instead be found in a body near him, or something like that.