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I just modded my 71- and got rid of the back-up lights as well. I've registered several older Vettes and all I had to do was show the guy where the serial numbers were and that it matched the title.
I could see them being sticklers about license plate lights but reverse lights?
Did a Law Enforcement Officer tell you this?
I live in Ohio and seem to get stuck in alot of roadside inspections and they have never checked my reverse lights.