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I believe that for an auto gearbox the reverse signal is generated by the gearbox control module rather than a physical switch like in a manual transmission.
In your case it is not happening and a fault code is not generated because it doesn't know the reverse signal is not being received.
The reversing lights themselves are driven by the footwell module I think so there could be a faulty connection to the gearbox module, the footwell module or one of the modules themselves at fault.
It's a case of checking signals along the line from the gearbox module until it disappears. Quite a diagnostic task ahead I'm afraid.
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