Headlight wiring harness issues. Please help

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The usual way to join wires like that is with crimps. For $5 you can buy a cheap crimping tool and box of 100 assorted barrel connectors in any parts shop in the US--but they are junk. A proper crimping tool (which will last a lifetime and make a properly tensioned crimp) is about $50US and the crimnps range from 25 cents each for "decent" ones (in quantity) to $1 for "marine grade" conectors that are also lined with adhesive and jacketed with heat-shrink. Once you use one of those--the connection is permantently sealed and watertight.

If you don't seal them, eventually water will get in and rot the wiring and they will dim again. For just 3 wires? I'd go to an auto or marine electrical shop that already has the good tools and ask them to do the job.