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Hello, my name is ***** ***** I am a professional here at Just Answer. I have noticed that your question was not getting a response and thought I would see if you still need help with this.I apologize for the delay and I hope I can still assist you with this here. The problem you are describing sounds very much like you still have a charging system concern and the problem is with low voltage. I would start with having the new alternator tested to be sure your getting a proper charging voltage with the engine running . Proper charging voltage should be right at 14 volts . While testing the charging system also be sure to make sure the battery tests okay and can handle a load.
Its not likely going to be a coil issue which would only effect the engine causing a misfire and not effect the lights. The engine has to have stored power in the battery to run properly and if the light where dimming then it sounds like you where loosing battery voltage. The place to start would be to have the charging system rechecked. Most auto parts stores will perform this test for you at no charge.