That looks like the one - all I know is it's the pin that has a permanent live running through it (I suppose that is why the windows can do their drop and close even with the ignition switched off). When it becomes corroded is when the trouble begins, imo. I suppose it's because there is always a live circuit in that connection that the reaction progresses.
It is logical conclusion and this corroded contact could be bad for short lift/drop and not too bad for longer lift/drop of windows.
Had this problem with mine - turned out the door had dropped slightly on the hinge & this was causing it to fail when in the closed position (although still worked in the open position). Realignment of door required to fix it.
It is logical too... Skewed door causes skewing of window support and friction between window and guide elements could be enough for trouble.
Maybe I should to mention one more thing: my problems started after machine polishing of my GT in local workshop. Maybe vibrations caused by polish machine were source of disalignment of window in guides?