Depending on how close your neighbors are, an air rifle with a pellet loaded, on a day off from work, during the week might be a better option. I had a neighbor to the west of me that eliminated a pecking nuisance off my garage eves with his .410, for which I was very grateful, but, that was two neighbors ago, and the current version would be mortified at the thought of it.
I had people tell me if I eliminated the bugs he was looking for, he would quit pecking. Sure. I think they peck just for fun some days, just like a cat that sharpens it’s claws on your couch, instead of the post you bought for him to do that to. Never found any bugs in the wood of the garage, just woodpecker damage.
Good luck.
Best,
Ted
It would be interesting to hang a hollow log or box that would be really loud when hammered upon. Might be all that's needed to get him off the house.