@1K9 Thanks, I see those on eBay.
TRIUMPH ROCKET III STARTER MOTOR SOLENOID REPAIR KIT ( 428000-1810 ) | eBay from the UK too so should be quick shipping. Interesting that the fault indication on the eBay item suggests you just hear a click and no starter motor turns. When mine is playing up, you push the starter button and don't hear anything (at least I don't think, will really try to listen). Also there is reference in the forum to the clutch lever switch being a bit ****y, where releasing the clutch lever slightly made it make connection and bike cranked. When I was troubleshooting earlier at the side of the road when she wouldn't start, I got bored of pulling the clutch lever while trying various things so I taped it pulled in and focussed on messing with the loom while jabbing the starter button, so I don't think it is that switch.