There are two possibilities, in my experience, either:
1) the wire is broken in the first few inches of the connector - either end and pulling on it or chopping it back may show you which.
2) the wire has broken inside the harness - for this, there is usually some sign of damage at some point.
If it is not (1) above, then the easiest solution is to run a new wire from the supply point to the device, note if this supply also powers other devices then connecting to both free ends may solve that issue as well...
The time and effort in opening the harness is not worth it unless there is significant damage that has to be repaired...
Edit: the other thing to check is that you have 12v both sides of the fuse - visually checking is fine but the element can fracture and the fuse looks good but isn't, so checking with a meter is necessary.