What signs and symptoms should I look for and how long after eating the button should it take for symptoms to appear?
A couple of days or a day. They will probably poop it out if it isn't too big. But if it is you'll know if it got caught up in their liver if they have these symptoms:
whining, lack of interest in food, lack of energy, yowling in pain , and they stay in bed a lot. If they show any of these symptoms, contact your veterinarian and tell him/her the problem. They will probably give you some steps to follow or prescribe some medication for the dogs. If it is that bad, they will preform a special surgery.
Good Luck!