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on your original Civic headlight there should be a main headlamp bulb and a dip headlamp bulb and then a small sidelight or parking light of 5W or similar
its this small light wiring that you want to wire to the new LED strip , the only thing to be aware of with LED's is that they are polarised, so have to be connected the right way round to work
so the positive feed from the side light has to go to the positve on the LED
as to extending the wiring then I'd 1st trace the wiring loom back into the car / chassis side a little to see if you can release a point where its been tied down / restrained and so remove that restraint to provide some movement and a little extra length
if this won't be sufficient then its a case of getting a soldering iron out and some heatshrink insulation to splice in an extra 6" or so of wire
this video may be of help
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