Windows 10 on external SSD - touchbar and track pad issues
The Boot Camp Windows Support Software contains files that should be exposed to the Windows installer early in the installation process. There is also software that can be installed after Windows finishes installing. You may have only preformed the after part. In other words, have you made sure all the INF-style drivers were copied to the driver store before the first reboot during the installation process.

When using the Boot Camp Assistant to install Window 10, the files contained in the Widnow 10 ISO files are copied to the same volume as the Boot Camp Windows Support Software downloaded from the internet. So when GUI Windows installer executes, the needed files (such as drivers) are extracted from Boot Camp Windows Support Software. There is no indication to the user that this happens. Also, when Windows finishes installing, the Setup.exe application included with the Boot Camp Windows Support Software executes. This is what users do see.


  Note: If the version of Window is sufficiently newer than the model Mac, then most likely the needed software will already be include with Windows. This is only a problem when the Mac is new enough that the needed software in only exists in the Boot Camp Windows Support Software.


You may want to try a normal install of Windows 10 to the external drive instead of a Windows To Go.