When the airbag module is powered (ignition pos. 1) it first grounds the warning light and after module self diagnostics go thru without problems it turns off the grounding on the warning light. So sounds like functioning normally at that stage.

So diagnostics working fully on all other modules?

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E39 530dA -02 M-Sport Messing metallic
E53 X5 3.0dA -06 Sport Stratus grey
E70 X5 40d -12 M-Sport Space grey