I had exactly this problem with the JCW Clear rear lenses when replacing a stop/tail yesterday.
There seems to be no reason to solder the bulbs in, other than greed ! - get a solder gun and solder-sucker - and desolder the bulbs !
I guess you could always get a set of normal lights from a scrappy and use their bulb-holders if you don't want to desolder everything !
Nobody at the Mini dealerships I've called seems to even know of their existence or be able to supply the special bulbs !!!!
So, the solution. Buy two rear facing White LED's (That glow Red !). Amazingly, got mine at Halfords in the (ahem, do not tell anyone) Ripspeed section (£12 !) - they look better than the originals.
I still cannot find anyone that sells the individual pearlescent bulbd (Plenty of chrome ones, but no pearlescents !)
How do the white lights work without reflectors - I know JCW used to sell them (now obsolete !), but where did they go on the car ?
BTW the dealers wanted about £38 a side !!!! - daylight robbery !