Does time machine backup my external as well?

TM can backup data from an external HDD, but it will not backup data from the same physical HDD it backups to, as that would be redundant and not a real backup, unless you have the habit (or people accessing your Mac) deleting your own files.

Time Machine FAQ

This is how I backup:

 

Yes, it will not be backed up, as far as I know.
To make sure, go to System Preferences > Time Machine, click the OPTIONS button and see, if you can either EXCLUDE the other partition of your external HDD or if that partition is already present in that Exclude List (if so, see, if removing it from that list is possible).
If you can't exclude the other partition or if it is already listed in the exclude list and you can't remove that exclusion, then TM will not backup the other partition.

If the above turns out to be correct, meaning TM will not backup another partition on the same HDD TM backs up to, then this is not a problem.

Maybe you oughta invest in another HDD if you value your data. HDDs will fail, some sooner (the moment they spin up for the 42nd time), some later (some humans report HDDs still being usable after ten years of use).