The above ebay item will not work with a 1st gen MIni not even a 2003 on with aux facility - it should be £5
The normal aux in lead for boost has a little circuit board in it that triggers the aux input into appearing.
The 2002 does not have aux in so my lead for this goes into the cd changer port & has a larger circuit board which makes the stereo thing it has got a changer connected & opens disc 1 track one for your device to play through