Ganpti23

I watched that youtube video of trains and lightening bolts. I asked: Please help. I haven't done any physics since O-level in 1987. Imagine there's another observer by having a lightening bolt detector in each end, synched to the same atomic clock, and by a miracle they are in exactly the place the lightening bolts strike. So those two detectors could record the exact time to the pico-second. {Or whatever it is.} What would the detectors say? Would it be like the lady as they are both part of the train's reference frame? Or is it different, as these two detectors, despite being on the train, are a different reference frame{s}? Or if Einstein says both observers are right, does this mean that you couldn't add this part to the experiment? Isn't observing like that with a pair of detector-clocks basically opening Schrödinger's box? And if so, surely we then find out which was right? Dear God, I'd love some help with this.