I have a 64 Skylark Convertible (first ever vert). The car has been in storage for a few years and when I hooked up power to the switch, the top slowly came up and stopped about 3 inches from reaching the top of the windshield. At that point it seemed the hydraulic rams were straining. When I unzipped my rear window, the top completed its cycle and all was good. Does this seem like the hydraulics might be a little weak? There are no leaks in the system.
Mine does the same thing, this might not be your issue but my rear window was installed way too tight. Therefore I never zip the rear window in, but when i do, I added another zipper (yes two zippers) then the window is way too loose. I try not to drive in the rain anyway. Also check your pump fluid level. Love the 64