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I picked another ordinary rear view mirror off eBay. Much to my surprise the fitting it different.
The stem ends in a female socket rather than a male ball (rightside of 1st picture) : the mirror has a ball on a stalk on back.
Now I can fit the dipping mirror I already have (not the one I got from David Pearson of http://www.canleyclassics.com/ that has a socket on the back) onto this new stem.
Job done!
David - thanks for taking the time to try to help. Problem now sorted. I never thought that
there would be so many variations on a theme. I thought Stanpart tried to standardise!
PS whilst visting Stafford TSSC International I noticed amongst the autojumble that there were plenty of rear view mirrors that could be bought and customised as I have done.