heres what you should do... go buy an auto relay 12v one. Hook that up to the detector and make the "SWTICH" one run off of the accessories fuse. Look on the fuse pannel for it. But, ground the other wire. But make sure you get an inline fuse for it cause the detector cst you money right? That plug that plugs into the cig lighter has a fuse in it. better be safe than sorry.
man there is a much easier way to do it rather than going out and buying something that you don't need. Just cut off the little thing that you would plug into your cigaratte lighter and strip the wires, pull them apart a little bit and remove your "audio" fuse there should be a fuse map located on the panel that you pull out. Just pull the fuse out place the positive (+) strip of the wire under the fuse and push it back into place, then just ground the negative(-) wire. Let me know if you have any questions.