BMW electronics don't make sense sometimes.
I'd recommend you go grab the proper wire harness and fog lights for your vehicle out of that Barlow picknpull for your body type OR grab the wire harness from the 4.8iS and wire that up then at least know that is proper and then rediagnose. BMWs cause.weird errors for what seems like unrelated problems.
If nothing else your wiring won't be a hack job.
Maybe the wiring used is of wrong AWG? I'd start with the basics.

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I swear, my cars are like a girlfriend.
Sometimes its a rough ride, sometimes its smooth motorin'.
Sometimes she doesnt like how i treat her and sometimes i dont like how she behaves.
BUT at the end of the day, she loves it when I am inside her.

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'91 850i
'05 X5 4.4i
'09 Clubman S