Absent evidence that a crime has been committed, is being committing, or is about to be committed, the mere act of a citizen participating in what is an otherwise lawful activity does not and cannot serve as a basis for reasonable suspicion.
For example, I'm sure that each TN municipality, indeed, the state itself, have laws that prohibit the operation of a motor vehicle upon public roads without a valid drivers license, yet absent the aforementioned evidence to the contrary, the presumption must always be one of innocence, rather than guilt, which prevents law enforcement from stopping motor vehicle operators merely to check for a valid license.
That's what you're missing. In Tennessee, subject to limited exceptions (possession in a car, for example), possession of a firearm is a crime under T.C.A. 39-17-1307. PERIOD. It simply is a crime. T.C.A. 39-17-1308 then has a list of defenses, which includes possession in one's home and possession in public of a handgun with a carry permit. However, keep in mind that a defense works differently than an exception in that it shifts the burden of proof. In the case of an exception, the officer must have PC of the crime itself and that no exceptions may exist. When a defense is involved, however, the cop has PC and can either accept a defense given or arrest the person and direct the person to raise that defense to a judge/jury.
As such, because of the way Tennessee law is currently written, the following could in theory happen. A sheriff could direct his officers to arrest every handgun carrier he comes across; and the prosecutor could take it to trial and make the permit holder raise the permit defense by showing their permit to the jury. Similarly, if an officer learns of a gun in someone's home, he could swear out a warrant under T.C.A. 39-17-1307 and arrest the person in possession of a gun in their own home. And then the prosecutor could take it to trial and make the person raise the "possession in the home" defense by showing their house deed to the jury. Again, I'll emphasize that possession of a gun in one's home in Tennessee is technically a crime; and being able to demonstrate that it is in the person's home is a defense to the charge, not an exception, which allows the prosecutor to force it to a trial if he/she really wanted to. Then, in either case, once they're acquitted, the sheriff could direct an officer to follow that person to the evidence room where they'll pick up their confiscated firearm. And once they sign out for it, the officer could then arrest them again for "possession of a firearm under T.C.A. 39-17-1307"; and the prosecutor could take it to trial and make then raise the "possession of an unloaded gun for transportation purposes" defense. And once that trial was over, they could continue that in an endless loop. In essence, if a Tennessee sheriff and prosecutor just really wanted to be absolute tyrants, they could in theory under current Tennessee laws harass gun owners to the point of effectively banning firearm ownership in their county.
Fortunately, I'm not aware of any county doing something that stupid (if they did, it would probably get thrown out as unconstitutional and likely get a good portion of the rest of the statute thrown out with it). But they could in theory do that. And that's why the law needs to be changed to where those defenses are exceptions. Doing that would make it similar to the other states and require more than just possession of the firearm to create probable cause. Quite ironically, possession of a firearm in a private motor vehicle currently enjoys greater protection under Tennessee law than possession of a firearm in one's home since possession in a car is an exception but possession in the home is a defense.