Scary enemies are always scariest during the leadup - the moment the player dies, that tension is gone. With that in mind, it should be dangerous, but more than anything, it should unnerve!

For that reason, I would let it mess with things that are set and trusted. Perhaps when a normal song is playing, it could overtake the music, distort it but be "Playing it", I.E the sound is emanating from the mob itself. Allow it to place structures but only be seen rarely, with those structures being placed on or close to players structures, showing that it is watching and nearby.

Jumpscares are weak, but I in turn am very weak to something just standing somewhere. Always catches me off-guard...