I have cedar shakes for the siding of my house (built in 1955) and over the 8 years I have lived here I have had to deal with woodpecker damage and holes.
They normally put the holes in the siding looking for bugs as you said. I have had them also put holes in the facia boards trying to get at carpenter bees. Nothing like sitting at my desk and hearing what sounds like a jackhammer trying to bore a hole in the house!
First you have to try to get rid of whatever bugs the woodpecker is trying to get at. I will bet it is probably carpenter ants or sugar ants under the siding. The ants may only be using the siding as a way to get from one place to another, and not necessarily infesting the wood in the area. That was my issue with ants. The carpenter bees, well, they made their tunnels inside the facia boards, and the woodpeckers were trying to get them out to eat them.
I sprayed insecticide all around the foundation of my house, plus on the siding leading up to the spot where the woodpeckers were putting their holes. I also put ant baits around the foundation of my house, as well as shoving them up under the siding wherever the woodpeckers were pecking.
It took awhile, but once the ants were gone, or perhaps started to use a different route to get from point A to point B, the woodpeckers stopped pecking the house in those spots.
I filled the holes with paintable caulk, and when it started to set up a bit I used a piece of extra cedar shake that I had and used the outside grooved surface to press some grooves into the caulk so it would hide the repair better.
Then I primed and painted it to match the house. I would not use silicone because paint does not normally stick to it.
I still get a random woodpecker hammering my house, but that is usually when we forget to put out a suet in the hanging feeder. I don't know if they hammer the house to tell me hey, we're hungry damn it! Or if they hear some ants crawling up the wall. Who knows.
But be diligent in finding out if there are bugs or ants crawling up or living in the siding. Once you get rid of that, you will get rid of most of the woodpecker hammering the house.
Jim