Follow the wire back to where it connects and rig up a jumper from your headlight connector to that point. This will bypass the questionable wire. If the headlight is now bright, it means that there are some broken strands near your original repair. The wires take a lot of flexing as you move the handlebars back and forth, so it is common for strands to break.
When a voltage regulator goes bad, you usually wind up with burnt out bulbs from excess voltage. I think your problem is more likely to be a poor connection somewhere. Also make sure the ground wire is good.
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2011 EC250E
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