You're starting from behind the 8-ball. You have very non-standard wiring and connectors, lots of apparent modifications and additions and it's not a good sign when you have toasted wires. There may be mayhem resulting from that incident going on inside the harness. The brown wires terminating in 1/4" female and male spade connectors may be associated with the OEM alarm (can't say for sure having never seen an installed alarm) but they are non-standard for a stock K75. I can see Scotchlok IDC connectors (which are bad news) that indicate PO additions.
Start by tracing back that burnt wire. If it disappears into the harness, then you'll probably have to start dismantling the harness to see where it goes and what collateral damage it has wreaked. If you can discern an insulation colour code, then report it here and we can probably help identify what it is.