He still needs to address exactly what melted down, and is now shorting that lighter plug circuits wiring harness, which now popps the fuse when he turns on ignition switch...
When I made the comment about the pl9t thickens, it was based on the results revealed about the attempts to jump the bike thru that socket, and results of that effort now.
With this bikes CANBUS system, when a wire melts down, and may melt into a ground wire in a harness, or a power wires for some other area, hidden 8n a wrapped harness, all sorts of signals can get crossed. Then, during the starting process, those wires may heat, and connect, and also disconnect once current flows, çreating this hard start syndrome..
At this point harness examination and repair is necessary, then, and only then, should the bike be analyzed thru some invoked diagnostics, either thru onboard system, or KDS, but only after the short circuit is fixed, and a fully charged battery is in place.
The cig lighter is easiily accessed, and can be pulled out with little effort, id start there and start tracing those wires back to the harnesses..
Alsso note, that circuit runs thru an accessory relay, and if that relay was damaged by a high current surge, like jump starting thru it, it could have latched that relay in a manner that is causing this issue... so id pull the fuse, pull that relay, pull the lighter, and see if these make an effect.
IIRC the relay lives on the left side, under the black filler plate or side glove box... on a gen 1 its the rear most relay in the bank of six that live there, I don't have a gen 2 new book, sorry.
I'll also ask this, where there, or are there, any accesory items connected to either of the accessory circuits, forward one, or rear one, this is important.
I ask, because if so, you sshould also examine those wires as they may have melted at 5he same time, creating 2 more points where a short co7ld have occurred during the jump attempt. All 3 circuits tie to that relay, thus if the bike was powered on during the jump process,, any one. Could have taken a hit.