I tried to hardwire my V1 without success today.
But I think I found the wire you're talking about! Because after the dome lights went out, so did my radar detector.

I'm still looking for the 12v accessory/ignition wire.
I have the dome light with map lights, sunroof, and navi. So, if you have this as well, it *should* be the same. If you take out the assembly, you should see two connectors, one 3-pin, and another massive one that houses many more wires.
On the 3-pin one, there is a turquiose wire (not the dark blue one). That is the positive wire. The dark blue one should be the ground. (check first before you start splicing!!!)
HTH!