External Hard Drive Won't Mount
I'd recommend checking if fsck is holding your disk hostage upon connection. This was it for me.

Running ps aux | grep fsck revealed:

root              2587   7.3  0.1  4363584  21780   ??  U    10:56PM   2:22.54 /System/Library/Filesystems/exfat.fs/Contents/Resources/./fsck_exfat -y /dev/rdisk2s1

So the solution was a sudo kill -9 2587 (insert your PID instead of 2587) (or sudo pkill -f fsck).
As soon as that ran, my Volume immediately mounted.

Oh the irony of fsck being the problem...

Addendum (surfacing from comments):
Ideally, you're better off letting fsck run its course. Otherwise, you'll run into this the next time too.