That could actually be an advantage for you when the time comes. Can you get it in writing? That would be better. Once they are officially out of the way it is just between you and the neighbor. You don't want them in the way when you block the sewer line to prevent further damage to your property.The city engineer, law department and board of health are sympathetic, but claim they have no jurisdiction because it's a private line.
That will get the neighbor's attention in about 24 hours or less. I'm not suggesting that you do it without notice, but just let the neighbor know that you will be solving the problem your own way if he mumbles, refuses to cooperate, avoids you, etc. Follow it up with a certified letter putting him on notice of your intentions.
The fact that he might have an implied easement is irrelevant; he is responsible for the line in any case and would be overburdening the easement (if any) by ruining your property by his uncontrolled effluent.

