Hello jcotrel1,
Welcome to the National Gardening Association and to these forums. The game camera is an excellent idea. I am making a mental note to buy one for my own use.
Since you haven't already seen the culprit(s) in action, there is a fair chance that their activity is nocturnal, and the guilty creature is a slug or snail. If your game camera isn't night-time capable, take a flashlight out at night and do an inspection of your caged marigolds. If slugs or snails are the problem, a product called Sluggo is a safe-to-use and effective bait to kill them. I guess you could also hand pick them, but I would want to use some kind of tool to do that.
Maybe just gloves would be sufficient. Keep us posted on what your game camera reveals.
ZM