Finally some joy on this issue!!
Here is my workaround (or solution).
On the Western Digital HD there was a .pdf buried on it with the real hint. That is the HD comes preformatted in FAT32.
So first I connected it directly to the Mac rather than the Airport Base Station. This allows it to be seen on the desktop AND read by Disk Utility. It also allowed it to be read by Time Machine. However I chose to reformat it in Mac OS Extended (Journaled).
Then the Time Machine initial backup was done through the Mac. When completed I plugged the HD back into the Base Station, went to Finder/Go/Connect To Server using the smb://10.0.1.1 address. Voila, The icon is back on the desktop and readable by Time Machine
I suspect this all could have been done without backing up through the Mac first. Just happened that is the way I did it.
The Key seems to be to reformat the HD to other than FAT32 for the Airport end of things. Seems to me that was the problem I had when I was backing up both PC and Mac to one HD. FAT32 as I recall will not work that way.
So a solution that works. May require the HD on Base Station to be mounted each time you power up. Minor inconvenience once you are going though.
Cheers
Geoff