Most of the adapter's I've seen for adding a trailer wiring harness, and put on my own vehicles just plug in between the tail lights and the rest of the vehicle. I've never owned a purely Japanese vehicle so I'm not sure how that works.
I'm wondering if there isn't a positive and a ground flipped around somewhere in the car where you spliced in? LED's don't work like a normal DC mono filament bulb where the two are interchangeable, juice will only flow one way through an LED. Could be that power is leaching through somewhere else in the fixture if it its a cheap one and that is the little bit of light that you are seeing. Not sure though. Like Carl said, check it with a voltmeter.
Really? f*cking wire nuts? Dude, solder it, heat shrink it, tape it. Wire nuts are only slightly better than the quick splice connectors. Its kinda like crapping your pants with a nice solid BM, or with the runs. Either way, you've just crapped your pants.
You do realize you're responding to an 8 year old post that was randomly bumped to the top by spam?