I get the sense that you are a police officer. If so, you are a police officer who is going to get your department sued. That, or you're going to blow a case some day by having evidence thrown out under the fruit of a poisoned tree theory.
Your legal latitude for "frisking" a vehicle for weapons in a traffic stop is officer safety, which is what allows you to check ONLY the area within the immediate reach of the driver. You are not searching for contraband. If the driver has already told you that he has a weapon, where that weapon is, and that he has a carry permit, he could have an arsenal in the trunk and you would have no reason to see it, or to look for it.
Now ... if (IF) the reason you pulled him over isn't a traffic stop but because both the vehicle and the driver potentially match the description of the guy who just held up the Stop-N-Rob 3 miles down the road, THEN you would be acting within Terry in a reasonable suspicion of (possible) criminal activity. But even then you don't get carte blanche to toss the whole car. Unless you make an arrest, all you have is an investigatory detention, and all you are allowed at that point is to search for weapons in the immediate vicinity that could be a threat to officer safety.
You need to have your supervisor bring the prosecuting attorney for your jurisdiction in for some departmental refresher training.
But, my friend, I know exactly what I can and cannot do and you are plain wrong on several facts. Yes, the purpose of the frisk is not to obtain contraband. Again I say, if you are a law-abiding citizen then the chance of your entire car being frisked is virtually zero unless you are at the wrong place at the wrong time. A frisk is not for finding contraband (although if you see contraband in plain sight while conducting a legal frisk it's fair game, but that's not the purpose of it). A frisk includes the lungeable area of the vehicle, which constitutes the entire area of the passenger compartment. This encompasses more than "around the front driver seat." You can only check where weapons could be present. The arsenal in the trunk is off limits, as it is not in the lungeable area.
Yes, a broken tail light is a motor vehicle infraction (in probably every state), but it still violates criminal statutes. An expired registration plate is a misdemeanor and an arrestable offense (although I've never seen or heard of anyone being arrested for it) in my state. There are reasonable suspicion stops for narcotics violations. There are speeding violations that are arrestable offenses. There have been a number of times that an equipment violation on a motor vehicle has turned into an arrest of the driver because the officer LEGALLY obtained PC for arrest during the stop. All traffic stops are potential criminal investigations. You originally said that no traffic stop is a potential criminal investigation and that is factually wrong. Look into the wren principle if you're not familiar with it (precontextual stops are allowed). As most have said, casual conversation and not freaking out will be your best friend when dealing with police. Even if you are nervous around cops, even when you haven't done anything wrong, most guys will be able to differentiate between that versus the "Oh crap, I hope he doesn't find blank" nervousness.
This would all be a moot point in the OPs situation, and likely anyone else posting on TFL. I don't take that there are many people who would portray a number of indicators of criminal activity here. There wouldn't be a terry frisk of the vehicle, I would likely just pull the pistol out of his bag and hand it (the bag) back to him. If I was familiar with him, I probably wouldn't even mess with it. If he was on the east side of town at 3 am and he shakes like a whore in church as he hands his license, can't tell me what he's doing on this side of town, and keeps trying to reach behind him after I'm already holding onto one gun obtained from him, then he might (WILL) get his vehicle frisked. It's all about context. I know what I can and can't do and you are wrong.