I am fairly sure that the vehicle mileage is stored within the lighting module & if you fit a second hand unit, it will activate a subtle "dot" on the instrument display that indicates to anyone who knows that.... something is not correct!
I had several units to play with on an E46 last year with a weird indicator fault. All of them worked, but I seem to remember the mileage displayed was different with each unit. In the end, my fault turned out to be the audio unit (wireless to you & me).
It turned out that a child had introduced several coins into the cassette door & they had caused all sorts of problems.