Not sure I've the ambition and energy to document the process of auxiliary 12-volt outlet wiring on a first-generation KLR, vatrader, but--been there, done that!
I wanted CONSTANT 12 VDC for my outlet (don't like GPS receiver switching to internal battery on stops), but--connecting to a "switched" + 12 VDC wire (the BROWN one) would be a similar process.
I used a genuine Wal-Mart auxiliary 12-volt socket, with spring-loaded cover, and a fused connection directly to the battery terminal.
Electrical connection is straightforward, but . . . mechanical? The KLR's relentless vibration is MADDENING! This "whole lot of shakin' goin' on" (apologies, Jerry Lee!) will FLING your plug from its socket, breaking electrical contact, every chance it gets!
I've used rubber bands as an inelegant work-around; haven't found the "sweet spot" to mount the socket with negligible vibration.
'Most anything works o.k., for occasional electrical connection, such as air compressor, etc.; however--under way with engine running, it's a different story.
Sensible, "right way" solution: Use connectors not subject to separation-by-vibration. You lose the convenience of easy automobile-style plug compatibility, but enjoy continuous connectivity. "SAE" plugs, polarized (have the + female lead toward the bike), and . . . I shudder at the expense, but "BMW-style" connectors offer higher reliability than automobile "cigar lighter" type connectors.
True confession: I haven't taken the positive-connector step myself, still relying on an automobile dashboard style plug-compatible socket. If you follow this path, mind the vibrations in the area where you mount your socket.