EDIT: Posted before I read Millhouse's post above; + 1, Millhouse!
Symptom changed to a true "no start' problem - so I messed up something while working on it. Is gnd at the blk/white wire at the mag. what stops kills the ign? Or is it killed at the CDI - or am I still totally screwed up?
BLACK/WHITE (exciter coil voltage) shorted to BLACK/YELLOW (ground), at ignition switch or engine stop switch kills the engine. The wiring insulation color may CHANGE, between a connector and a component; be wary.
Normally, with the ignition switch ON and the engine stop switch in the RUN position, the BLACK/WHITE ground is lifted. With ignition switch OFF or the engine stop switch in the STOP position, the BLACK/WHITE wire is grounded; as mentioned, the engine kill mechanism.
Myriad possibilities; hard to diagnose by remote sensing; maybe you could give Bob at TPI a call, asking for a referral to someone cognizant of KLR electrics.
BTW, the Canadian headlight lamp, with relay harness, sold by TPI is DYNAMITE for Generation 1 KLRs. TPI, I think, knows its way around the KLR circuitry, or knows of someone who does.