It's likely that they're drumming on the gutter because the metal is loud. Drumming is both a way to get at food by digging under the bark and a way to signal for territory+mating. The signaling is the main reason that the drumming patterns are distinct!
I used to put suet cages out. Then I'd walk outside on summer mornings to find my porch and gutters utterly destroyed. Finally figured out it was black bears that came in the night trying to get at the bird food.
Amusingly, it wasn't until I put the feeder out (with suet and a bunch of other seed) that he started drumming. It wasn't right away; there was about a year or so where the red-bellied just came for the food. There were several different males and females back then. Now, I'm pretty sure it's just him. I've read that they can drum like this in part to mark territory, so maybe he's just trying to keep the food for himself. He still has to duke it out with all the other birds though. Can be pretty entertaining.
And fortunately, I'm usually up by 4 or 5 am anyway so he's never woken me up, but yes, he's banging away really early.