Sounds like you really don't want to get the neighbor involved in your household business.
If the computer in question is a desktop with a wireless card, just remove the card. If the responsible party replaces the card, remove it again. Even simpler, most of the cards have external antenna that screws into the card, just remove that. Cards cost money, and they will soon find the cost-effectiveness to be negative vs the ability to ogle.
Have teenagers who believe anyone's access point to the net is their exclusive property. Developed a small collection of cards and antennae, but their cash flow could not keep up. They can now go on ONLY when I say so.