jvb
I'm not aware of any provision within the Act for court action in the event that the Act isn't enacted.
In the first instance, a (party) neighbour's only recourse is an injunction. This can be incredibly expensive, with no guarantee that the plaintiff will be awarded costs. And legal advice must be sought before proceeding down this route. That said, the merest threat of an injunction is often enough to focus minds on the provisions of the Act.
Subsequently, if a party was to proceed with works to a party wall without instigating the act, and if damage was to occur to the neighbour's property, precedent suggests that the courts will find in favour of the neighbour - even to the extent that the burden of proof will be on the defendant!
Whether or not the OP is a busybody or nimby and whether or not nimbyism is a good thing (I happen to think it is), none of what I've described above would make any difference to them - it's not their wall!
In the present situation, 10 months have slipped by with apparent inaction on the part of both the OP and the party neighbour, so I wonder if the courts could be bothered to intervene in this instance.