John F. Mc Carthy bought my Lincoln new in 1964. At the time, he lived in the Beverly Hills house pictured above.

According to the guy I bought the car from, Mc Carthy owned the Beverly Wilshire Hotel (below) in 1964. So far, I have been unable to verify this.
The guy I bought it from claimed he bought it from a Hollywood movie rental lot. He said it was used for the interior shots in the Matrix.

He pointed out two details as proof: In the film, the rectangular lights over the rear seats were replaced with round lights (see above photo). He said when he bought the car, the lights were still removed. The second detail was that the rear driver's side door jam had been painted silver to provide more reflection when shooting the film in low light. It was still silver when I bought the car and there was no apparent reason for anyone to have painted it this way.

I know the film was shot in Australia, and the car in the film is a 1965. But the 1964 and 1965 do share identicle interiors and it is possible that they shot a few scenes on Hollywood sound stages. I doubt it though.