Why do Japanese beetles cluster around my gutters and drain pipes at dusk? Is there a repellent spray?

Heat. They are getting cold and they are attracted to the heat produced by the exposed metal of your gutters and drain pipes. If you find or develop a spray to keep them away, you'll make a fortune marketing it. Only way I know of to get rid of them is to kill them. Try a 1/3 of a pouch of chewing tobacco in a pint jar of water allowed to sit for 3-4 days until the water looks like tea. Spray this water on the bugs around your house. The nicotine in the water is a contact poison and should do the trick. Good luck.