Got it. The consensus is that I should fumigate my neighbor's building when I do my own. As I said, I was leaning in that direction since I'm tired of dealing with him. So that is what I will do. Thanks to all for the advice.
But I'd like to be clear on the legal principle. Is this consensus because I don't have a legal leg to stand on (i.e., I can't make my neighbor fumigate his own building), or because this isn't worth the legal hassle?
And to get at that point, answer me this. Would the advice be the same if things were reversed? That is, what if my neighbor wanted to fumigate his small termite-infested building that was attached to my termite-infested building but I took the same position he is taking? Would the advice be the same — that if he wanted his small building fumigated then he needed to pay for my building as well?