2003 Chevy Impala Intermitent auto door locks and back up l

I have an intermitant problem with my automatic door locks. When the car is started and I move the shift lever to reverse and/or drive (on the column) the door locks do not automatically lock. I can lock all the doors by pushing the lock button on the door. When I stop and put the shift selector in park, they will not automatically unlock. A couple other things that will not work as they should when this happens is I DO NOT have back up lights. Also, I can't open the trunk when I push the button under the dash, with the car in PARK. The only way I can use that button under the dash to operate the electric trunk opener is if the ignition is in the off position. After varying lenghts of time (weeks to months) all of a sudden all will start working. One other thing I notice when it is NOT working properly, I hear a single CLICK from under the dash only when the brake pedal is released, never when I apply the brakes. Sorry for the long message, but I wanted to give as much information as possible. I would appreciate any help or suggestions! Thanks, John