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The light being on dimly is due to a difference in voltage between the ignition circuit and alternator regulator.

What type of relay are you using? I'm guessing a constant operation solenoid?
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If Im understanding this right, I think where you have tapped into is a Yellow Black wire at the alternator? Probably not the best place to go, Looking at the diagrams in my book this is the...

It might tell you if charging two or just start battery.?
Multi meter will give you some more info