Does you neighbor actually like having the vine there? Or do they just not want you using toxic chemicals on their property?
There are ways to kill a plant that don't involve poisoning it, such as cutting it off from the base. Maybe you could approach your neighbor and be like, "hey, I'm concerned about the way that vine is growing all up on the power lines. Would you mind if I just cut it at ground level so it dies back and doesn't cause more problems with the power lines?"
The vine bush isn't in the pic I posted. Those are the dead vines in the pic. 30 feet to the right he has a vine bush thats working its way back to the dead vines. The vine bush is like 6 feet tall, by 10 feet wide, by 1 foot.