If it was an auto ferry, I recall riding on it between San Rafael and Richmond in the forties and early fifties. The completion of the Richmond/San Rafael bridge spelled the doom of steam ferry boats on that route. If it was a passenger ferry, I have no personal history.
George H. Harlan published a book, San Francisco Ferry Boats in 1967. On page 171 he states that the Berkley was built in 1898 by Union Iron Works in San Francisco. It was sold in 1958, moored in Sausalito and used as a store. (Spell that as tourist trap). I had been on it when it was in Sausalito to see what was left of it. If it has been moved and towed to San Diego since would have slipped by me as I haven't been in Sausalito since the early 70's. Besides the Berkley, there were other auto ferry boats on the San Rafael/Richmond route and as I remember the names of some of them: Sierra Nevada, Russian River, Eureka and maybe a couple( Tamalpias, Redwood Empire?)of others whose names have slipped my memory in some sixty years hence.
Bill