I think, by now, most citizens of countries outside the U.S. know the self preservation driving rules when driving in America.
Long before these two recent incidents I would, if pulled over by the police, stop the car engine, handbrake on and place both hands clearly on the dash board so the stopping /approaching officer can clearly see them irrespective if he had drawn his weapon or not.
If asked to produce my D/L or passport I would politely invite the officer to handcuff me with my arms behind my back and then tell him which pocket they can be found by him or his colleague.
As all colours in some of the states in the U.S. are allowed to carry concealed weapons then it defies logic that as a gun carrier you would start reaching for driving documents when an armed police officer approaches you with weapon drawn !!
Perhaps rules of conduct and engagement should be part of driver training in the U.S. as well as don't leg it if you have been stopped for a broken stop light.