Hi all, an update. I took the headset off and had a look at the ribbon cable and printed circuit that's attached to the back of the speedo. What's happened is that some numpty previous owner has taken the speedo out from the headset cover, but when putting it back in has forgotten to carefully pull both sides of the printed circuit through to avoid pinching it when refitting the top to the base. Basically, both sides of the circuit ribbon have been crimped when the headset has been put back onto the bike

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I also found that the bike has never been touched in 3000 miles from 2003, apart from the headset. All four headset threaded inserts had been overtightened, splitting the plastic surrounding them. And the offside mirror mounting had been overtightened thus stripping the thread

. I ended up helicoiling it myself to get the stem to fit properly, and I do now have mirrors.
To fix the indicator turn signal I had to tape the printed circuit ribbon almost back on itself to get it to make a connection, and it now does work. I added an indicator buzzer at the same time too, and was pleasantly surprised to find the wiring had already been provided by Piaggio, so that was an easy job

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I've refitted the broken headset top for now while I get a plastic chrome replacement resprayed in the original Vintage Green. Thanks for the advice wack63, it helped a great deal

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