Both browns come from the same fuse so doesn't matter if you mix them up. There just needs to be a separate wire for the heater and the signal so that readings are not affected by a voltage drop. This is not going to fix the A/C though.

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1988 325is (purchased new) sold
2004 X5 3.0 2005 X3 2.5
2008 X5 3.0 (new to me)