OK first up I have no idea what a zodiac mini light is, or which 5 pin connector you're referring to.
If the light you've purchased only has 1 wire it's earthing through its mounting point - what've you got the light mounted on? Disconnect the battery terminals and use your continuity tester to check the connection between the light's mounting point and the negative battery lead. Then turn your ignition switch on (with the battery still disconnected) and check the connection between the positive battery lead and the supply wire of your light. The wire on that light should of course be connected in parallel with the tail light LED.
A couple of LED replacements for the 12v light are
these licence plate frames with LED illumination by Radiantz, the "Lite'n Boltz" licence plate mounting bolts with LED's in them by DEI, or the same idea by Kuryakyn, all on the same page.
