Does it have a license plate on it? Even an expired one? If so, then it was registered under somebody's name back then. I don't think DMV records are public documents, but it can't hurt to ask.
Alternately, you might be able to find out from city/county records who owns the property the Airstream is sitting on, and start from there. You should be able to find that out from a plat map, which I think is public info, since every real estate agent seems to have one.
Engineering: Finding complex solutions to simple problems you didn't even know you had.