Ok.
An important correction from my friend, who knows much more about Japan than I ever will
"Your explanation of the purpose of the converted order is however a little foggy, though I doubt whether many readers of the forum will notice. An obijime is the accessory itself, often made of coral, ivory or a combination of pearls in a silver setting, fixed upon the rope. It functions like a brooch for ladies in Europe and has merely a decorative function. The ropes you show are obihimo's ropes to keep the obi in place during wear and not obijime's, and finally the obi you show is for a yukata. The obi this obijime is intended for is the wide, thick piece of cloth, often very decorative, that is wound round the waist of a women when she wears the formal kimono."
I would like to thank him for this interesting and important correction!
Cheers,
Nick