You bring up an important side issue.  You don't know if the officer stopping you just recently experienced a shooting event.  I learned the easy way (by not thinking and being stupid) about keeping my hands in plain sight.  When I get stopped, I pull my wallet out of my back pocket (left hand) and hold the wheel w/my left hand (w/wallet in plain sight).  Then I reach over to the glove box (after stopping, by the way), get my car's papers (registration and insurance) and place the right hand (w/the paperwork in plain sight), let the officer see my hands are full of wallet and paperwork, then I get out of the car and go to the rear and wait for him.
  An officer once asked me for my wallet and I reached for it too fast and when I had it out and looked up, I had a 9mm pointed halfway at me (and on it's way back to the holster).  I don't do stupid things like that anymore plus I always keep my hands in plain sight now while moving slow.
  Officers have family that they want to get home to, like the rest of us!  I certainly don't want to do their job (w/my sterling personality, I'd last about 1 day before being fired)
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QMC, USCG (Ret)
The best luck is what you make yourself!