I may be making some progress!
Here is a pic of the assembly... but assembled in the other half of the casing. The clue should have been the fact that the power lead had to be screwed into this side of the casing when I first started. Also, the rotor locking button was fiddly to say the least during my first efforts!
When the power switch and wiring is attached this other way around, the unknown black wire hangs fairly naturally toward the central part of the casing near the stator as correctly predicted by Theobald with guidance to reassemble and look again from Tronde and Helius - many thanks for the ideas!
The curve still makes me wonder but having placed it there, tried it and it worked, i'm not complaining. So, EMC, some sort of noise filter (the white block ceramic?) for the circuit?
Now that it is clean and reassembled, hopefully correctly, and at least trying to turn when switched on - I have another problem.
So, it kind of wants to turn but needs a push to get it started and then starts sparking quite a lot inside near the brush ports.
When I push harder on the brush retainers, it seems to lessen the sparking a bit but I have to turn it off after a few seconds because the smell isn't great.
Before I turn it on again and break it, do you guys/gals think changing the brushes would be a wise next move or does it seem worse than I fear?
There seems to be plenty of depth to the brushes but I know they have less than optimal design. What is the spec length for 398/400 brushes, I wonder?
Anyway, wanted to keep you all updated as to progress.
Maybe some other noob will benefit from my lack of experience with electric motors.
"I tried it the other way and it worked!". Not universally the best advice* at all times but on this occasion, at least, it holds true!
*e.g. Specific Polarity Devices, Wives, Motorways - the blacklist is endless.
If this is indeed the solution to my original problem, I can only apologise for the simplicity of the solution and the simple-mindedness of the problem's author.