The whole glove box routine should be avoided. Fumbling for docs under stress is not where you want to be. Better to keep your insurance/registration in an envelope in the visor.

That's why you put your hands on the steering wheel. The officer walks up to the car, sees your hands, sees your wallet on the dash and puts 2+2 together.

Otherwise, when you reach behind your back for your wallet, the officer has no idea what's going to be in your hand when it reappears.