It does sound like separation anxiety, in that separation anxiety means just what the words say. Obviously it isn't the really neurotic kind, or you wouldn't be able to leave him anywhere, so count your blessings, I've heard of some dogs who are much worse than he sounds.
I don't know if even a slight change in routine would make him behave this differently, all dogs are different in how they react to and deal with things. Since it seems kind of mild, maybe it would help if your parents did something with him, took him out for a walk or played a game, took him to a drive thru for a burger, something that would occupy his mind for awhile.
Other than that I don't know. I've read about training methods for SA, but they were for dogs who got anxious any time their owner would leave, and took a lot of time with leaving in increments and coming back a few minutes later, ect. I don't know if you have time for that when you're just running errands.
I don't know if even a slight change in routine would make him behave this differently, all dogs are different in how they react to and deal with things. Since it seems kind of mild, maybe it would help if your parents did something with him, took him out for a walk or played a game, took him to a drive thru for a burger, something that would occupy his mind for awhile.
Other than that I don't know. I've read about training methods for SA, but they were for dogs who got anxious any time their owner would leave, and took a lot of time with leaving in increments and coming back a few minutes later, ect. I don't know if you have time for that when you're just running errands.