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The application materials will say what evidence you should submit.
I can't see any reason why they would need a copy of your driving license. Driving around Italy in a hire car is a completely normal thing to do. Having a driving license is completely normal. You don't need to prove things that are completely normal. Everybody knows you need a driving license to drive and nobody would claim they were going to drive if they didn't have one.
And, just for a moment, pretend that your application is all a big lie, you can't drive a car and you just said you were going on a road trip so that your visa application would look more realistic. Pretend that what you really want to do is live illegally in Italy. Is forgetting to include a copy of your driving license really going to be the only clue that you were lying? It seems unlikely.