Personally, I would make up a test light to replace the fuse so you don’t keep blowing them. A “smoke test” is certainly one way to do it, but you risk further damage to the wiring harness.
Pick up a “power on” test light from one of the auto parts places, similar to this:
Get a couple of male .250 spade connectors and crimp on some leads that are several inches long.
Pull the #3 fuse and plug the spade connectors into the j-boxes’ fuse clips. Narrow the width of the spades (if necessary) so they will fit into the fuse clips.
Alternate to the above "packaged" test light if you have a soldering iron/gun and minimal soldering skills, would be to get a single filament 12v automotive bulb, and solder the leads from the spade connectors directly to the bulb.
Connect the spade’s leads across test light and turn on the ignition. Due to normal circuit loading (without a short circuit), the bulb may glow dimly.
Begin to manipulate the harness (yank, tug, pull, etc.) at various locations and look for the test lamp to go bright. This will indicate that the short has reappeared.
That brown/black wire out of the j-box only goes to so many places (igniter, kill switch on the RH handlebar switch cluster, instrument cluster), so concentrate your harness manipulation in those areas. Obviously, temporarily install the tank (with the ignition on and monitoring the light) and jostle it back and forth looking for a change in lamp brilliance.
FWIW - power comes out of the kill switch as a red wire. It goes to the start pushbutton in the same cluster, and to the coils. If the switch is in the "run" position, that "short" would transfer through it back to the fuse. The coils are under the tank, so I would look very closely at those leads and their routing.
That’s the best I can offer. Good luck with it.