So not exactly what you suggested, but I will be adding some randomness(probably not to the zoomies) in at some point. So I initially thought to base the player around a Great Pyrenees as that's the breed we own. They are notoriously stubborn. Super intelligent, but not the best at obeying commands.
So my stat system contains a stat called stubborn that when you start the game is at 100 and will eventually get lower as you level up. My plan is to come up with some mathematical formula using the stubbornness stat where if it rolls a certain value range, I'll flash some dialog about the dog heard you, but just begged for cheese instead or something like that.