mini r53 button under the radio left side close by gas pedal , what is it for ?

That appears to be an addition a previous owner added as that switch is not mini equipment. that change holder that its attached to is commonly used to hold a number or aftermarket switches, aux ports etc as it has easy access to the stereo and engine bay wiring. Try switching it on and off with a partner to try to locate it or trace the wiring if it's driving you bonkers.