Quote - The hints have led me to a guess ...

My desktop PC has a CD-R/W drive ... with a volume control.  The volume control is a knurled control and peeks out from a small slot in the face of the drive.  ... Dimensions of the opening are about 17 mm X 3 mm ... since your "item is less than an inch high and less than half an inch wide or 20mm by 8mm" ... and mine is about 1/2 that size ... I'm still not sure. 

Could it be the volume control on the CD drive of a PC? 

OTOH, you have already said that the item in your image does not rotate and the volume control does rotate (or at least ... slide) ... soooo .... maybe its the play or eject button. 

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Martin

Close but still not 'On the Button' as the saying goes.