Woodpeckers are not damaging the siding in search of insects. The holes are almost always in the top one-third of the building.
The woodpeckers are usually ones that are called sapsuckers. It has to do with putting horizontal and occasionally vertical lines of holes in the siding and hoping that sap will rise in the holes and they will basically get dessert. If the holes are singular and large, woodpeckers will attempt to chip out a nesting area.
Since the holes are not insect related, pesticides don't work. Your choices are either to block their access to the sides of the house or to try various methods to scare them away. The best method is to block the woodpeckers from the top third of the house with something like netting or screening. it needs to cover the area and not be so close to the siding that Woody can hang on it like cargo netting and peck away. It may be possible to use something like cup hooks or small eye bolts on the underhang of the house and attach bird netting or some kind of small screening. This will keep the woodpecker away. A product like bird netting that is used to protect fruit trees could work.
Or you can use any number of scare tactics but they have to be changed periodically or the woodpecker gets used to whatever it is. These are things like a home-made version of scare-eye balloons. Thses are just yellow balloons with two target symbols drawn on with a marker to simulate two eyes.
Or it could be strips of aluminum foil wrapped around a string that blow gently in the breeze. Or it could be disposable aluminum pie plates hanging on strings. The message here is something that moves in the breeze and is shiny to attract attention. Iit is not about sound. It is about something that is able to move silently... the most dangerous of predators. But when Woody finds out that it is always the same old thing, the scary item is bypassed.
Wind chimes don't work because all they do is make noise. Cardboard owls don't work because they don't move. Birds see movement and not objects.
Usually, wooodpeckers seem to enjoy houses in grays, browns and tans that appear to look like a big stump to their tiny brains. But changing the color of the house is no guarantee your little friend will stay away. There is always a woodpecker that appears to be color blind.