mattwnz:Do the neighbors have a sewage easement across your property? It should be on the title. As others have said you need legal advice.
It won't necessarily be that cut and dried. An easement may exist without being recorded on title.(IANAL)
Personally I would consider the cost of the repair. If it was significant I wouldn't discount the opportunity to cost share. The existing arrangement has survived 50+ years. A new PVC line would last even longer.