To be under the gun means to be in a stressful situation that requires quick action, which is what he was feeling when he fished in the glove compartment.
Consider the statement "He fished in the glove compartment, feeling stressed because he had to act quickly, and brought out shane's wayfarers.". Based on this "He fished in the glove compartment, under the gun, and brought out shane's wayfarers." a true statement? Yes, no, or I don't know?