Further to this, I took a button off my GS Mini and did some measuring with a digital calliper. With the button off we have a shaft 7.5mm long, with a diameter of 4mm, with 2 opposing flats that measure 3.5mm between them. The button itself is 10mm between the ends of the central hole which takes a screw 14mm long with a thread diameter of 2.45mm.
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