So, if I understand you correctly, you CAN unlatch the seat with the nylon tie and raise it, BUT even with it RAISED, there is still no movement of the switch or cable in that direction. Correct?
If so, then that pretty much narrows things down to an internal problem with the switch, or the cable itself. Not much help from my end if it is internal to the switch without a switch replacement. But I have had occasion to need to screw with the cables up under there.
The cable end at that end of the cable is a sort of cylinder shaped bead. It slides into the socket at the bottom end of the switch assembly. Because the whole switch rotates from side to side with the handle bars, sometimes it just slides out of its socket under the right conditions. The cable that locks the glove compartment when the front wheels are locked, is notorious for popping out of the socket.
So, if this happened suddenly to you - meaning one day it's fine and the next day it's stuck - my sense is that the cable end has tried to slide out of the socket beneath the switch and is sort of jammed in place. If you take enough stuff apart up, you'll be able to access that area beneath the switch and be able to check it out and possibly pop it back into the socket. Investigate and see if you can feel any movement of the cable down at the latch end when trying to turn the switch. Also, possibly trying to operate the switch with the handle bars fully one direction or the other might allow it to pop back into place.