Why not simply remove the plug from the amplifier, apply some WD40 to its contacts, and then push the plug on and off 2 or 3 times to clean the contacts. It looks like the lady may very well have found your problem. I had a cold start refusal which I traced to the amplifier plug, and another member (doz) recently reported a misfire problem which he cured by cleaning this connector.
http://bxclub.co.uk/forum/viewtopic.php?t=6873
I don’t think it’s very likely that your autochoke is the problem. The autochoke performs several functions, but the particular malfunction which could cause cold start refusal is very easy to check. The choke flap is the one which stands straight up when the engine is fully warmed up. With the engine cold, you should check that it is fully down in the completely closed position. You should now be able to push it with your finger into the full upright position. It should feel reasonably free and when you remove your finger the flap should spring back to the fully closed position. If for some reason it does not fully close, then this could cause cold start refusal.
Solex carburettor in my BX19TRS
As a matter of interest, if you had bought the spark tester that I recommended in your earlier thread, you might have been able to use it to easily verify if the fault was caused by spark failure. When the engine refused to fire, you would simply pull off one of the plug leads, pop the tester over the plug, and plug the lead on to the top of the tester, and then try starting again. If the tester does not “flash” , then you would know that there was no spark and then you would not need to speculate about the autochoke. It only costs £2.89 inclusive of postage.
http://cgi.ebay.co.uk/The-Legendary-Ora ... dZViewItem
You can see the orange spark tester in use in the bottom left corner of the picture above.