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IF you use the key FOB and the backup lights come on, then the #38 micro relay and the 15A appraoch fuse in the underhood fuse panel is good.
If the reverse lights don't come on when the stick is in reverse, the first culprit and common fault is the backup light switch mounted on the transmiisson. When it fails it becomes internally grounded and when this happens it blows the #21 backup lamp fuse in the passenger compartment footwell.
Most of the times when the backup lights don't come on the fault lies with the backup switch. To check the wiring, you can short the contacts in the backup switch connector. If all circuitry is good the lamps should light. Let me know how you make out. PM me if you want.