Every October, there's references to Cthulhu in the Blood Beetles Shack but there's no real sightings of anything tied to Lovecraft's works in the event.

Due to Cthulhu's area being R'lyeh out in the Pacific (specifically 47°9′S 126°43′W), I was thinking a more region appropriate sighting that could work is Nyarlathotep in his avatar of God of the Bloody Tongue: https://lovecraft.fandom.com/wiki/God_of_the_Bloody_Tongue

I don't know if coding would allow this sighting every five years but maybe as a rare encounter with the chance of finding a larger amount of blood beetles than most encounters give.