I have seen a couple of pictures of this concept car from 1960. It appears to be a 60 Fleetwood 4-Door Convertible with an "inward folding" top mechanism. Is there a source where any detailed photos can be found? I am fascinated by this car!
Although I will not be very helpful to you, I do recall that the car you are describing was featured in a monthly issue of the Club's Self-Starter magazine several years ago. The photos revealed a gorgeous automobile, and Cadillac had reportedly toyed with the idea of four-door convertibles upon learning that Lincoln was introducing their's to the marketplace. The car was quite well-done, and the end product was tasteful. I had not recalled that the roof frame was "inward folding--" but this interestingly became a Cadillac feature on the '71 through '76 Eldorado Convertibles. I wish I could be more helpful. :)
I believe there is a fair amount of information and photographs concerning this car in Roy Schneider's terrific book, "Cadillacs of the Sixties".