I don't think so. They *did* carry vacuum all the way to the back of those cars, but it was for a vacuum motor that opened and closed the rear vent, and for the optional 1964-66 remote trunk release. (They're called tee-birds because of the number of vacuum lines that terminate in a golf tee by now, rather than at some excessively fanciful accessory.)
The convertible top is a story all its own (literally -- if memory serves, the repair manual is available as a separate book of some 40 pages). It was run by a hydraulic pump powered by an electric motor (some serious amperage made a near 20 foot journey to the rear end of these cars). This was controlled by an array of actuators and limit switches and so forth that was worthy of an airliner's landing gear. The driver only had to push a single button, though, and this could be done at any stage in the opening or closing process -- kinda like a garage door. Four and a half decades have not necessarily been kind to all this stuff. Enterprising inventors sell modern replacements for some of the more unreliable and/or downright scary electrical elements.
--Joe