Stop Hazel then unmount the external drive

I'd like to stop Hazel and unmount the external device it utilizes for storage. I also want to reverse the process, so Hazel starts when that drive appears.
They operate perfectly when I use them from within KM. When I stop KM, they always fail.

Can anyone make any suggestions?

You shouldn't need to do this. If a drive is unmounted, it should be fine (rules won't run/succeed). When you remount it, Hazel will notice it and act accordingly.