Yepp, you are right on the additional facts, and reasonable suspicion - why not sleep at the rest stop?
It was also reported that he had some empty gun cases in plain view in the back seat, which then led to the search of the trunk.
"At the trial the jury was told about the exceptions under New Jersey's gun laws. Under those laws firearms do not have to be registered, nor is a permit required if they are merely being transported from one place where it is legal to have them to another place where it is legal to have them. However they must "be carried unloaded and contained in a closed and fastened case, gunbox, securely tied package, or locked in the trunk of the automobile in which it is being transported."
"Police testified at the trial that the SUV did not have a trunk, and some rifles and shotguns were in unlocked nylon or vinyl cases on the backseat of Reininger's vehicle. They testified that the handgun was loaded and in the glove compartment, contrary to federal law."
His car was an SUV and it's not clear form the story if the long guns were in the second row seat or in the wayback. I wonder if he had the best legal representation. Also, he was tried and convicted in absentia. That probably didn't help him.