I've never heard of an operating system on an external drive. It was formatted to MS flat. I repaired it copied pasted the files to my MacBook and than the drive broke while putting the files back on it. The files on the original copy were bad so I think the drive was on the way out.
Some if the files are lost so I suppose it's moot, but I was curious as to what happened.
I guess I'm used to working with clones so thereby the question. I clone my whole system to my external. Occasionally they need repair....the OS is on there.
I'll leave this post to others more familiar with what you are doing.