I would first use an OHM meter, remove fuse for yellow wire, remove yellow wire from alternator.
Set ohm meter to 5k or similar OHMs then touch one probe to yellow wire connector and the other probe to Ground, 0 ohms or very low ohms means a short to ground in that wire.
Move wire around and see if you can "break the short", ohms will go up very high or meter will show N/C(no connection).
If you can break the short then start unwrapping harness to get to the short.
The reason you want to do this and not just run another wire is because if one wire in the harness is shorting out then wires near it may be suffering the same fate, i.e. there is a reason that wire shorted, could be too near exhaust or got chewed on by a critter, or...........?? don't know but it would be good to find out why it shorted.
Short could even be in/under fuse box
If you don't have and can't get an OHM meter then use a 12volt test light.
Remove fuse
Remove alternator harness
Hook test light to yellow wire and other end to battery +
Assuming yellow wire is shorted to ground the test light should light up
Move wires around to break the short