I know very little about these boards but slowly more information is coming in. It was given to me by my wife's father who bought it at a garage sale. Apparently a company called Jet Board Corporation sold the boards starting in the 60s. I don't know how many are out there, or much other information, but I now know they sold for $1700 + tax when they were new. Here's what else I know:
The hulls were made by an aeronautical company called Sargent Fletcher in El Monte, California. I had an email from someone recently who's father worked there until 1990 and was part of the team working on the Jet Board. The engine was derived from a McCullough chain saw engine. He thinks there were between 600 and 700 made. He's doing a little more digging so I should have some more info soon.
I was told by email that Steve Gould, the curator of the North Shore Surf and Cultural Museum, was a lifeguard at the Kahala Hilton the day the first motorized surfboard was demonstrated in Hawaii. He said that these boards were the result of Alfred Bloomingdale's (heir to the Bloomingdale Department store fortune) distaste for paddling a surfboard. He used to come to Waikiki to play. The prototype was made of wood and was unsuitable. Later models were made of aircraft aluminum by an aircraft company in California. The working model debuted in1965. Bloomingdale died recently, but Robert H. Krewson of Waikiki, who worked on the development is still around.
Jet Board Corporation was located at 9255 Sunset Boulevard in Los Angeles. I am not exactly sure when they went out of business. The below image is from the original advertisement for the Jet Board, courtesy of www.powerboarding.com.