Without knowing the exact issue or what's on the plug it's hard to give good direction, but here is the first thing I would try.
If it only blows when the plug is plugged into the backbox then it is probably not the harness, but something from the backbox connection to somewhere in the backbox.
Get you multimeter and set it for continuity (buzz when shorted)
There are 2 commons, One for 6 volts and the other for 24 volts.
Connect one side of the meter to the common that is connecting all of the lights together and then touch the other end to each of the plug connections.
See if you get a short. If you get a tone then it's one of 2 things. It could be the actual wire that is the common or it's your problem.
You can always disconnect the wire and see if the fuse blows which tells you the definitive answer.
Now you have to start digging and trying to trace the color.
You then have to do it for the common on the 24v side. You can usually find it by looking for a common wire running between the coils of multiple switches. The same test and results apply here.
Couple other things about the 24v side. When checking continuity you will get a tone when going thru a coil.
You can narrow down if it's a coil or a true short by checking the resistance.
Coils will have varied resistance while a short will show zero.
Hope this helps.
Bert