The number of problems are limited. Weak pump, bad cylinder(s), bad ground, dry hinge points in the frame, binding due to alignment, bad switch (resistance), bad wiring between switch and pump, kink in the fluid lines somewhere.
When I restored my 70 Challenger convert a few years ago, the top frame assembly had sat outside for a while. Big mistake.
The cylinders were so stiff that the top wouldn't go up and down smoothly and I destroyed a brand new pump.
New pump, new cylinders, new lines and then everything worked great.