http://www.imcdb.org/movie.php?id=59431

Unknown, make, model and role. Pics from extracts in youtube.
Here driving Frank Sinatra


Here driving Dean Martin

The first car is a 1964-65 Lincoln Continental 4-Door Convertible. The second one is a custom-built 1965 Ford Mustang known as the Zebra Mustang, built by none other than George Barris. His official site doesn't have it, but this one does.
http://www.ponysite.de/mustang_zebra.htm

Scroll down on this site, and you'll find it here too:
http://www.ilovegetsmart.com/cars.html

I don't know if it's a good expression: "You hit the nail on the head" (??)...but you dit it.
In second Ddey65 link, we can find:"Another Mustang -Z The Zebra Car- was used in "Our Man in Leotards." According to Smartian Sue, the car was created by George Barris, who's resume includes creating the Munster cars and the Batmoble. The Zebra Car has seen a lot of mileage, appearing in" Marriage on the Rocks" with Dean Martin and Frank Sinatra."

Lately Mr. Barris is becoming famous in my latest post:Supervan; The Van
Thanks Ddey

Done:
http://www.imcdb.org/movie_59431-Marriage-on-the-Rocks.html