At the end of the day, your dog is the one that is reacting aggressively. The fact that he's getting stared at is not a reason to react in that manner. I'd just work obedience and teach him commands not to react in this matter. Although eye contact is usually a bad thing, some people will claim that some dogs do it to incite play from others so to blame the other dog doesn't do anything for you in this situation. It's also probably not right to be going to your neighbor and letting them know that their little terrier is staring at your big bad shepherd and they need to teach it to stop doing that because your dog (who's freaking out at the fence) doesn't like it.
I'd really start working a lot of obedience with him in the yard while BFF watches. Teach your dog to ignore BFF and soon enough you shouldn't get that reaction.
Just wondering...does your dog react like this to passing dogs? Or is it just the neighbor's dog?
CD RE TC HIC 7/10