I normally have it set to 'Always show all icons and notifications on the taskbar' but I did play around with those settings just to be sure and still, no safely remove icon wants to show itself..
I have noticed though, I can safely remove flash drives by going through My Computer>Right clicking on the device>selecting Eject. But with any portable HDDs this method isn't possible, it would seem the icon is needed for that.
Very strange problem 