If you have power from the fuse but no to the lights
the most likely cause is the reversing light switch has gone faulty.
The fault is in the switch itself, quite common on this age of car, the dash lights and rear lights are worked off the same contacts on the back of the switch, replacement is the usual answer,
Check the fuses Check the backup switch Check the wiring - make sure that there is good contact.
check fuses Try turning your light switch back about half of a click until they come on. The switch probably needs replaced
Assuming you have replaced the bulbs with no joy and the fuses are good, your problem may be linked to the Neutral Start Switch on the side of the transmission. This switches on that circuit when the transmission in in reverse. Many times the contacts inside it become worn or dirty. It can be disassembled cleaned and re lubed or simply replaced. Hope this helps.
The flasher unit is placed in back of the fuse panel. Look towards the left side for its exact position.
Its probably a problem in the wiring to the lights themselves. Just follow the wires back until you find a problem in the wire.
short in electorical system
Check your fuses. The best way to locate and identify your fuses is to consult your owners manual.
Could be a couple of problems, one lose wire in pig tail harness, but since you say its both back up lights it may be a relay switch when you place into reverse the switch does not respond to activate the lights
Start with checking the fuses and bulbs. Then trace the wiring from the back to the front looking for damage, corrosion, loose connections, poor grounds, etc.
check your fuses
have you checked the reverse lights switch?