There's the possibility that US BMWs made in South Carolina are
different to Bavarian ones.

Always read the owners manual before you buy a car. I won't buy one
unless happy with the list of trailer weights under "Towing". "Towing"
in many car manuals just explains how to move the thing when it breaks!
John found the right solution to this problem: DIY.

The Isolator can't be used as an adapter. It must be installed in the
towing vehicle, as it requires a separate +12V supply for the trailer.
It should be able to synthesize a brake light circuit using the central
brake light of newer vehicles that are "4-wire". In this case both red
and amber trailer lights would come on for brakes.

Jim