Today I took the timing sensor out. Lots of buggerising around: I replaced the breather hose that runs under the spine from the headstock to the back of the motor a while back. It seems I made a "tactical error" in the process. The cable from the timing sensor went up between that hose and the frame, and the connector was hidden under the airbox. The result was that getting the sensor out involved "unclothing" the Le Mans all the way down to unfastening the airbox. When it goes back together, that plug will be nicely accessible on the frame just above the sensor, don't you worry.
The sensor didn't look too bad, but it will be swapped out. Holding the new one against the old one, and assuming they were both the same length in new condition, it seems the old one has swelled and shortened such that it is about a half a millimetre shorter than new. That would be enough to take the gap from (assuing it was correct) about 0.7mm to about 1.2mm. Going by what I have read here, amongst others from @guzzler's report on the subject, that would be enough to make it run badly. Whatever, the new sensor will go in.
Cleaning up around the sensor was a pain. There were liberal amounts of some sort of silicon sealant involved, and getting that all cleaned up took a while.
Since the airbox is now unfastened, the list of "things to be done now" has grown again. I wanted to just put the new sensor in, and see how that affects the way the bike runs. Since I'm so far in now, it seems sensible to go at the "tank off mainenance" thing again from scratch. I've been through that once already, but it was all a bit perfunctory. Since I've got it all apart again, it seems sensible to go at it again and take a bit more care about it. Cleaning the throttle bodies really properly, for instance, And I've got some new rubbers for between the throttle bodies and the motor. And I've got a new timing chain here, and whilst I'm in there I could repair the two broken screws of the four that hold on the alternator cover.
And the tailpiece is off, to make it easier to get to the screws for the sidecover. Since that's off, I could have another look at the wiring under the seat, particularly on the underside of the relay sockets. And while I'm in there, I could consider adding the additional relay to supply direct power from the battery to the starter solenoid.
The fun never ends...