You cannot pass annual inspection without working reverse lights, period. We are pretty weird with our laws, like you MUST have working wipers, but windshield/windscreen isn’t required. We aren’t nearly as strict about things as MOT. For example, I’ve passed with only 3 lug nuts once.
What probably happened was the previous owner had transmission work done recently and had no clue that it didn’t work because they can’t see it when driving, and it didn’t need an inspection. Something probably got knocked around/unplugged during service. I had that happen to me once.
I do recall however, my reverse camera, it will activate just fine, but if you need to drive forward and then back, it may not turn back on, but will if you shift to park then reverse.