External USB drive won't stop after shutdown
Solution 1:
Also, I re-read again before posting, and I think I mis-interpereted your question. By after shutdown, do you mean after the PC shuts down, or the process of shutting down, before the PC turns itself off?
I am assuming you have a PC, not a laptop. When you shut down your PC, there s still some power flowing through the SMPS (also called the PSU). Thats the reason you can see the hub lit. As for the HDD, it might be connected to the same spike-strip/board as the PSU. After you shut-down the PC, turn off the wall socket too, and see if that works.
Solution 2:
It's not possible.
Here's why: Because your drive is set to run as long as it has power. There is no way to change that, it's hardware level.
So, the only way to make it stop that is to unplug it.
Apologies if that wasn't what you wanted to hear, but it's the truth as far as I've been able to figure out.