Hi Val,
Like you, I would always want to comply with the law. It sounds as though you were badly advised by the lawyer who acted for you in your purchase. You don't say whether it was the vendor or agent who told you the signature could easily be obtained from the neighbour, but your lawyer should have made it a condition of your purchase that it would not proceed until the vendor had corrected the legal status of the pool, thereby making them responsible for obtaining the signature, not you.
We were in a similar position when we bought our house - a first floor extension had been built with planning permission, but the record had not been updated at the Land Registry. Our lawyer insisted this was corrected before we paid the 10% binding deposit. The vendors were able to do this quite quickly, but it cost them around €1,000 - not just Land Registry fees, but also for IBI (Council Tax) arrears where they hadn't been paying for the increased living area.
So where does this leave you? You could try to do the same to a prospective purchaser that happened to you. I have a feeling that wouldn't sit happily with you - and you also run the risk that a purchaser's lawyer picks up the land registration issue and advises their client not to proceed without you, as the vendor, correcting the situation first. Effectively, you would be in the same position as you are now.
With the state of the judicial system in Spain, I doubt that suing the agent or your lawyer is an option. So I think I would research abogados who are Horizontal Law specialists, to see whether there's anything that can be done to force the neighbour to sign, or recourse in law if they refuse. It also makes me wonder how this would be dealt with if, for example, the neighbour wasn't refusing to sign, but had died before he was able to do so?
My abogado is a country (rural land) law specialist, but I will ask her whether it's possible to identify a lawyer who specialises in Horizontal Law. I'm assuming this could be done through Alicante's Colegio de Abogados, but it will be quicker to ask her. As you say, what you don't want is someone who is happy to just keep charging you for sending letters.
Kind regards,
Kim