Based on everything you described about the guy's behavior, the location, his reaction to 1) people entering the store and 2) your gun, as a dispatcher I would absolutely send 2 units to check him out. His tats and general appearance doesn't do much to tip the scales in his favor either. He may have been a noncustodial parent there to pick up his kids and the ex-wife was late, or a laborer meeting his boss to get his paycheck, or even a junkie/hype waiting for his dealer to show up (or he was the dealer waiting for his buyer) or even some random guy from craigslist waiting for a blind date at KFC. Regardless of all those possibles, there's nothing wrong with having someone check him out and see what happens.
I think I would have taken my meal and eaten in an unobstructed corner of the parking lot to see what happened.