OK, I have looked for two days for at least a picture of the back of the connector to the TCM on my 2006 XK8.
After troubleshooting the faults P1637 and P1643, I have found that the problem has to do with CAN faults between the ECM and TCM. Under the car, there is no back, or shell, to the connector to the TCM, set at the back RH side of the transmission. The pins and wires at the back of the connector are therefore exposed to the weather (and winter salt water, etc.). The car has been extensively detailed, including under the car, so I expect that cleaning fluid has been applied to the connector as well.

This car has 60K miles on it, and looks like it is still sitting on the showroom floor -- yes, even underneath.

The problem is intermittent, and the car runs beautifully, until it doesn't. Then it shuts off, and we go to the side of the road. Ignition OFF, then re-start, and all is OK. One other case is that twice I have returned to the warm car after it has been sitting for a while, and it won't start. Only after sitting and retrying for 10 or 15 minutes does it fire right up, asking "yes, what's your problem"? It has once, after the above scenario, started in Performance is Limited mode. Took it home right away, then turned it off and restarted. It was ready to go, and seemed unable to understand why I am concerned. Runs like brand new, again.

Has anyone else been treated this way?