Hi there Daddywags,
Sometimes, external HDDs could make clicking sounds if enough power is not provided to them. This is why, it may be a good idea to try using different USB cable.(try another power cable as well in case the HDD model requires it)
If the issue persists though, then I guess that the drive has most probably failed as digitaldoc already suggested. If this is the case, I doubt that you will be able to access it with some HDD testing software. I guess it will not hurt to try.
In case the data stored on the drive is really important, you will need to contact a data recovery company.
Cheers,
D_Know_WD