What's causing my ST1300 to wiggle?

I have a Honda ST1300, that’s in generally fine fettle, with good tyres and swingarm, and with steering head and wheel bearings in good condition, too.
However, when pulling away, the bike feels like the back end is doing a little wiggle. I even thought that the engine bolts might be a little loose, but no joy there either. The last idea I can come up with is that the universal joint on the shaft drive is past its best.
Panbloke, MCN forums 
 
If it was the universal joint playing up there would be an audible ‘clunk’ when you opened or shut the throttle. It’s possible the wheel is buckled or the tyre isn’t seated properly on the rim, but if that was the case I think the ‘wiggle’ would get worse the faster you go. There is one other possibility – that the rear tyre tread has got out of line on the tyre. In that case the increasing centrifugal force as you accelerate may ‘flatten’ out the effect. Spin the rear wheel and see if the tread is centred.