How do I backup an external HDD using TimeMachine?
Make sure the external drive is some flavor of Mac OS X Extended format. 

If it's not, wipe it and reformat it or use another tool to back up those files.

Once that's done, make a couple of sample files on the drive.

touch /Volumes/whatever/test1
touch /Volumes/whatever/test2
tmutil isexcluded /Volumes/whatever/*


You can see what exclusion rules might be causing the test files to be backed up or not backed up. The manual page for tmutil will show you how to add and remove exclusions that the UI won't show you. 


On OS X, what files are excluded by rule from a Time Machine backup?