Well ... the epiphany failed. There's nothing inside the pivot (the black item in the pictures) I could latch onto, tried a whole bunch of alternative drive shapes, nothing worked. I did put a small screwdriver down into one of the channels in the circular wheel and used it as a lever to move it clockwise, the connector moved like it was moving apart, but appeared to be constrained by a latch in the other side and a small latch just to the left of the locking pin (there's a small gold mark next to it in the picture). This requires engagement at three places - the back latch, the front latch and rotating the wheel. I don't have the extra sets of hands to do that! There must be a master latch release, or maybe a special tool, to work these connectors.
Right now I've decided I can work around this connector being still engaged. I've unclipped a number of connectors and anchor points to take the strain off the harness with the facia removed. I've rotated the facia around this point on the passenger side, giving me enough room to do the rest of the work to make it tow compatible. When I've installed the towing baseplate I will hang it from its top mount and reach behind it (I hope) to reconnect the items I've disconnected. Not ideal, because I need carefully cut holes in the lower part of the assembly for the towing attachment points, but I'm hoping I can do it without making a mess.
Meanwhile, here are some more detailed pictures of the offending connector.
