Well, the daylight is over, and I'm more confused than ever.
I had thought from what I saw in the photos above, that the plug was missing. The parts diagram in the links above provided by Allans1100, showed the bottom of the ignition barrel with a short cable and a 4 pin plug.
I decided to pull off the plastic so I could get a better look. I had an inkling from the 'electrical tape' that someone had removed the plug and the socket from the wiring harness and had hardwired the two together. Perhaps the cable had gotten damaged, and this was their solution, rather than paying a grand to buy a new wiring harness, and slogging through stripping the bike down and replacing it.
When I got enough off the bike, this is what I was greeted with:
The cable had no plug and ran along the frame to the fuel tank where it disappeared. (If you look closely, you can see a boot which was probably clear originally just past the arrow head. My thumb is touching one which is very similar. In the boot were 4 sockets, with 3 plugs connected, one of which was the cable running from the barrel. I wouldn't realize this until later.)
Pulling the cable through, I figured I had surmised correctly, and I began to pull off the tape wrapped around the cable. To my surprise, I found a cable which was not joined, but was whole and still covered with the black factory cover.
I'm now feeling I'm a parts diagram noob, and perhaps the diagram isn't exact. The length of the cable may run from the front to the back of the bike, but to put that in a diagram would be a pain. I personally expect that if the cable is long, but represented in the diagram as short, it would have some sort of cut in the cable to indicate that the entire length of the cable isn't displayed.
Also, if you check out the diagram on the linked page, there is an arrow and F-19/F-22/F-42/F-45 beside the plug. I supposed that perhaps that shows that the cable/plug ran down to the location of the bike related to that diagram, and it would appear there. But the diagram for F-22 is the pillion passenger grab handles. There is no indication or reference to the ignition barrel cable/plug.
So I spent some more time looking around and staring blankly at the parts diagram, and I came to a realization: The diagram is all about ordering new parts, not explaining where things go. The ignition barrel and cable can be bought in a group of parts (in this case, the group is in a box, which is numbered '5'). These parts include the fuel tank cap, the lock barrels for the pillion grab handles, the barrels for the locking pocket (pie warmer) on the left fairing and barrels for the panniers. These have nothing to do with the cable, but everything to do with the key that is supplied with the ignition barrel. So they are shown on the diagram, as they can be purchased in a group.
All this time the bike was working correctly. I periodically turned the ignition to on and everything initialized correctly. I couldn't walk away from the bike splayed across my garage so I put it all back together. I only had one spare screw at the end :-D. I decided I'd turn the HISS light off, as I had previously, because the ECU reset had probably changed that. I turned the key and *hangs head* it failed.
So I'm back to the drawing board. Either the cable is broken inside, it's not the problem but something else is, or where it connects to the ignition barrel is worn/loose. I didn't get enough pulled off to access the barrel properly.