Follow these steps to get Windows running on your external drive.
Download WinToUSB
WinToUSB serves the same function as Windows To Go, an enterprise-only tool from Microsoft that doesn’t work with most consumer versions of Windows. It’s intended for use with USB sticks, but it will work for other external drives too.
Might not work out for you according to this.
eSATA might be able to work though since its not USB if you want external drive to have windows. Other thought is that the system have a drive in it with the boot hooks on it for say Windows 10 and Windows 10 is off onto an external drive that is using a symbolic link for C:\windows, so that the contents of Windows 10 are on the USB external but the boot hook and to get symbolic linking to work and USB drive support remaining on the internal drive.