How Do I Show External Disks on Second Display's Desktop?
The external display is not set as a mirror of the main display but rather as an extension of it.  So you can drag the external drive icon (or any file/folder/window) from one display onto the other.

However, this will not 'stick' as when you disconnect the drive and reconnect it, the system will mount the drive icon back onto the primary display (the one with the Dock).

Also, when you disconnect the external display, the system will move any files/folders/icons that were showing on the external display onto the main display.