Spider roof worm/wheel gearbox assembly
It will be the plastic worm and wheel gear inside the motor/gearbox assembly. If you are reasonably confident with mechanicals, you should be able to take the motor/gearbox assembly off the mountings/cables and try the manual switches then. If it cycles OK, then re-attach to the mountings and it should work OK as the gears will be meshing at a different location. If this still doesn't work, I would take the complete motor/gearbox apart (it's quite simple really), clean it all up and inspect the wheel. It is probably worn and sticking.
There are replacement wheels available, made from a superior plastic, but I would have to research where I got mine from now!
I have a 2001 3.0 litre Spider which was doing the same thing. Tapping the side of the motor just 'adjusts' the position of the worm/wheel assembly so it will then cycle.