Sorry, but this is far above my knowlege so I behave clumsily, I fear.
...this is where Linux comes into its own: the learning curve and the community. You're not on your own here
Okay, let's go down the checklist again to see what we missed:
issued fdisk -l
in the console, can you see the external drive? What is its name?
Issued umount /dev/sdb
likely sdb is the external drive
If you're not root, the command could be "blackholed" by bash without feedback, fdisk does that on my machine
. I issue it and ... nothing.
If you can unmount the drive...but it powers up again. So it could be a persistent process (Xorg is one of them, it dies and comes back for more), okay, let's look at /etc/inittab, list it and look for the word "respawn" - those are the respawning processes. Is the process for the external drive in there?
I'll do some more digging here...the plot thickens (never understood that one