Even though the aircraft appears to be abandoned, I would start with the legal aspects before sinking any $$$.
Local governments may have the right to dispose of dumped vehicles but, you may or may not have the right to acquire. A lawyer would know and perhaps an Aviation Lawyer might be a safer bet due to the Federal aspects of aviation.
Check if there is a data plate on the fuse and go from there .
If the original C of A document is missing, that may also cause problems.
You could probably go under experiment class if a problem arises but, I am out of my depth in that area. Ask a certifying authority ( engineer).
It is amazing how people claiming to be owners pop up once you start spending dough that you would not be able to recover if their claim is correct.
Unless it has historical value or some rarity ,it might be better to walk away , let it rot and find a safer bet.
A shame, I know.
Good luck