Welcome to the forum.
These are sometimes tough ones. I'd immediately suspect the trailer plug, it has both parker (instrument light) and reverse light wires in it. Those two circuits don't really meet up anywhere else - perhaps the stereo head unit if you've had a reversing camera installed, but can't think of anywhere else.
There are a couple of other things that can cause the trouble. Faulty/dirty bulbs can cause erratic issues, so check the tail lights.
It would be worth testing the tail light continuity (resistance to the chassis) on both the brake/parker bulb and the reversing bulb. The body of the bulb's socket will be earth, but the contacts shouldn't. If there is one that is very high resistance, you've got a wiring problem - and again, back to that trailer plug.
Easy way to try that trailer plug is to disconnect pin 2 (should be a black wire) - which should be reverse. See if the instruments come on. Pin 7 should also be examined - this is power for the trailer clearance and parking lights.