Sounds like the passenger side latch/sunroof cable. Not an incredibly rare problem, though (knock on wood) mine hasn't given way yet. If you catch it early and don't continue to try to operate it with the broken cable, it can be fixed by just replacing the cables. Some folks keep going with trying to open it and it "torques" the top mechanism and bends/twists it, requiring replacement of the whole sunroom part of the mechanism (crazy expensive).
The top appears to operate normally. The images on the link by rkw don't show the cable. Using the image, in the first one, there is a dotted line going from side to side, (drivers to passenger) that approximates where the cable is. However, I just went out to attempt a picture and I believe that it is a batten used to support the top approximately an inch or two in front of the black cable that actually IS connected on both sides almost immediately in front of the first bow.
If the cable isn't listed in the parts catalog, then it isn't available separately and it is included with a larger part (the top cover? I didn't completely understand your description). Perhaps a repair is possible but again photos would really help to understand the situation.
Crossing over to the NAM site I was able to determine that the cable is actually part of the top. I have temporarily relocated it to the center and will see about gluing in place when the sub zero temperatures we are having go away.
