First, make sure you are using EXT4 file system on your drive, and it's on /etc/fstab. Then you could see if mounting your HDD to your main steam library location on your home dir fixes the issue.
It's always a good idea to check steam logs to get a better idea what could be going on.
The issue tracker is here: https://github.com/ValveSoftware/steam-for-linux/issues
If you filter issues with keywords "external library", you have 68 open issues to compare to yours. Eg. one is a shader pre-cache issue, disabling shader pre-cache may help. In another one people report needing to run a console command to mount the external library.
Hope this helps.