Bulbs have been replaced so that's not an issue. Other rear lights fine so fuse should not be an issue. I checked the wires near hinge of trunk. They appear to be in good condition.

For some more context, License plate lights were also not working, replaced bulbs and they are working fine now. But same solution for Back-up lights did not work. Any suggestions on what should be my next step?

 

Check the wiring harness where it transitions from the chassis to trunk lid. The flexing of the wiring during trunk use can cause the wires to break.

 

Wiring harness looks in great condition. Did not open it up to check the wires inside. Is there any thing that needs to be checked under the hood? Any other suggestions?

 

Have you checked the bulb socket grounds?

Or determined if 12v is going to and from the back up switch. If auto trans the switch is part of the Park/Neutral switch on the trans.

Input power wire is Red/Blue. Output to bulbs is Red/Black.