2005 infinitig35 sedan reverse lamp will light up why

did you have someone stand behind to see if they flickered when R was engaged?...what I am getting at is what we need to know is the switch powering? or is it dead? Take a look at your fuse block to find the reverse lights fuse, when that comes up okay, look at the bulbs...strangely enough they have a set life (perhaps 3000 hours) and when their time is up (you must be spending a lot of time in reverse) could blow at the same time because of it...would take a good long look at the geometry under there to see if the switch is simply disconnected, transmission mounts are out of place causing this switch to not be engaged....but this is not rocket-science and something is causing this to happen....perhaps with a little clever investigation we can figure out why~