I'm assuming an automatic shift.
If you move around the trans shifter lever does the light come on and go off? Almost sounds like the switch is slightly misadjusted or it's worn. Move it around a little between Park, Reverse and Neutral without releasing the handle and locking it into gear (key on, car not running, e-brake set.). Have someone watch the reverse lights. See if you can find a spot where the lights come on.
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