The way I did it involved removing the cluster. Which is easy anyway.

I have no clue what you mean by a light on the center stalk. The switch can take a light for the rear fog inside the switch. Thus when rear fog lights are on, the orange light at the center of the knob will be on. US models do not have rear fog, so it will not work. On a Gen II the icons around the switch do light up. It out, lamp replacement needed.

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1991 560 SEL / 185k miles
1992 750il / 17k miles - project car