If the car was first shipped to and sold in California, it likely would have been through what then was known as Cal Sales, Inc. Unfortunately, that company is long gone, and I doubt any records would still exist (unless some CA Triumph club and/or member somehow managed to get hold of them).
It is also likely that you will see Cal Sales mentioned on any build certificate. Again, this was one of several regional distributors around the US at the time; they, in turn, sent cars to individual dealers. So those distributors, even if they still exista and have records, would probably only be able to tell you to which new car dealer a given car was sent.
