Yes, just add a wire that does the same as the switch.
You could use a small relay to bypass the button entirely or measure the voltage across the button pins when on/off and duplicate that with an output(power or ground, maybe a resistor needed) that you have available.

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