This is a common failure of the neutral safety switch. It is located just above the transmission pan, on the driver's side, rear corner. The photo shows the terminal end of the switch. A fast way to verify the switch is causing this is to turn on the ignition switch, crawl underneath and unplug the three-wire connector, then use a stretched-out paper clip to jump the two outer terminals in that plug. If you watch very closely and see tiny sparks when you make the connections, that is because current is flowing to the back-up light bulbs, and they are working. If you cannot see those little sparks, you will need a helper to let you know the lights have turned on, or you will need to look for yourself.
There is a thin metal gasket on the threaded end of the switch. It usually sticks there and is hard to remove, so be sure the new switch comes with a new gasket.
Images (Click to make bigger)
SPONSORED LINKS
Saturday, November 17th, 2018 AT 6:55 PM