Sometimes insects like Mason bees or Carpenter Bees, or other solitary bees will go up under the exterior course of shingles use the spaces between the interior layer to deposit their eggs/larva. This could be what they were looking for.
Exactly. This time of year there are cocoons to be had as well from various moth species, and some butterflies and moths even overwinter under the peeling bark of trees or anything that resembles the shelter offered by bark, such as wood, vinyl or metal siding.
I don't recall now if there was any particular insect suggested... my memory has more holes below the waterline than it used to have.
One of the "solutions" he had resorted to was trying to pick the woodpeckers off with a cheap air rifle fired from an appropriate window of the house. While this minimized his chance of hitting the house itself, it was more than a bit difficult to open a window or screen without the woodpecker(s) simply flying off and returning later. Someone observed him in the act of leaning sideways out of a second-story window, holding on to the casement with one hand and taking fast, wild, one-handed shot with the other, leading to an account of which entertained the town for days.
(He was a large gentleman though not of an athletic type, and was well into middle age. In short, he had made a spectacle of himself.)
He admitted to me that he never actually bagged a woodpecker... which was just as well, considering the legal issues.