T748's plan appears sound.
The unused wires he suggests as control voltage for the relay are called the "City Lights" conductors on KLR wiring diagrams.
I would "second" T748's recommendation to use a chassis ground or separate wire to the battery negative terminal to ground the lights, rather than exploit the ground wire of the City Lights circuit for this purpose, because--the City Lights wire may not be adequate for carrying the return from two 55-watt auxiliary bulbs; the conductor was only intended for low-amperage "marker" lights.
A good chassis ground would be located near the lights to minimize wire voltage drop.
The City Lights wires will be fully adequate to activate the relay, but questionable to carry the full current of two 55-watt auxiliary light bulbs, IMHO.
A chassis ground should involve bare-metal contact, free from paint or corrosion; or--use instead an adequately-sized wire direct to the battery negative terminal.
For '08 and later KLR's, you may use a splice to a BROWN wire as + 12 volts to activate the relay (BROWN is active when the ignition switch is ON). For a ground to activate the relay, a BLACK/YELLOW wire splice or chassis ground will work (o.k. for controlling the relay, but . . . the lights should have a separate and more robust ground for full current, IMHO).