would check brake lights come on when press the brake pedal, if no lights then would be something to do with it, as system senses the brake light circuit for reference, same as clutch pedal has same thing,, also to gear linkage is senses by a two way gear shift sensor on front of gearbox on manual trans and common failure, also any sack in gear shift can cause same thing ie dont get enough travel within gearbox selector fork as that sensor is a magnetic type and senses the selector through the gearbox as such,, below link is what it looks like
also the wiring for this can get damaged around the chassis leg harness area, its a ball ache to get at , with bmw own diagnostics tool its possible to live data this sensor and other sensors so see if they work correctly when using start stop, also if a battery is over 3 years old they dont tend to give enough stored power for the system to keep working as they are designed to never allow battery to go flat while sat in start stop as such, its the kind of fault i try and avoid due to time involved and mine field of maybe's,

Genuine MINI Gearbox Neutral Sensor for Stop Start R56 R55 R57 R58 R60 - 7601993 | eBay
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