check the reversing switch ,
remove the jack plug from the reversing switch, bridge out the wires on the loom connection  lights will come  on permanent  does the fuse BLOW ?  if NOT change the reversing switch.  if YES problem could be the reversing lights have  corrosion internally in the units,  or the wires leading up to them  have corrosion, check  the wires for  chaffing where they pass through holes in the car body.
                
 wirecutterman
                
 November 2009