project utilizing dimmer wire

well depending on the settings on the lights, id test if the 12v feed for the dome light changes when the light comes on and goes off, or if it's only the ground side of things, if its only the ground then you're just gonna have to tap into the ground circuit of your dome light. The easiest way i see is to splice into your 12v and ground from the dome light and use them to power the neons, In theory that means that the neons only get 12v of power when the dome light does therefor giving you the effect your after. e.g coming on when the dome light does