Discussion post 250 words and two scholarly sources

A police officer stops a car for failing to signal a turn. Upon talking to the driver, he discovers he has a suspended driver’s license and an outstanding warrant for Failure to Appear in court on a similar charge. The officer has no probable cause or reasonable suspicion that any other motor vehicle infractions or criminal activity may be afoot. He decides to tow the car as it is stopped on the side of a highway and cannot legally be left parked there. The front seat passenger in the car is the driver’s father, has a valid license and appears sober and otherwise capable of legally and safely driving the car. The driver asks the officer if the father can drive the car home. The officer refuses and calls for a tow truck. Prior to the tow truck arriving, the officer performs an inventory search of the car and discovers an illegal gun in the trunk.
Should the illegal gun be admissible against the driver? Why or why not? Support your answer. If you have experience with how this is handled in your jurisdiction, share that as well.