If your good with a volt meter it's pretty easy to trace the circuits....
The SX is notorious for breaking wires at the CDI mounted on the battery box if it's been beat on. I use to jump allot, bending swingarms etc etc and when it started doing funky stuff, I found broken and bare wires at the CDI under the electrical tape, just a thought............
The connections at the clutch cover provide a ground, so there ought to be a hot at the light at all times, I'd have to look at the diagram to be sure.
Do you have a daigram? MonroeMike has links to all the manuals
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