Does your neighbour still live in the house? if not you could possibly assume ownership of the house and the car
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I assume it belongs to the land owner or is at least there at their behest, If the land owner has no knowledge of who owns it then it should be reported as an abandoned vehicle, it may even be stolen?
You don't have to be the owner to be the registered keeper but you would still require some form of proof of ownership, if challenged by the police or DVLA
In the 90's My former boss rented a unit in Gifnock that had been lying unoccupied for a few years and there was a dusty old 1970's Alfa Romeo GTV, he couldn't find the owner or trace the previous tenants and applied for the book, restored it and kept it, however he was lucky.