It sounds like a game camera is what you need. I have 2 primos game camera with IR flash, and they take great night time photos, even better during the day. Also the day time video is very good; night time is good enough to ID a thief. If you worry about the small led lights you can just put a small piece of black electrical or duct tape over the light and no one will ever see it at night. My one recommendation is that you get the camera that has the most IR flash LEDs that you can afford.
The wild boar in front is about 8 yards away the ones in the back are about 20 yards.
This is just a fun picture, the bird actually landed on the camera, distance about 1 foot.
Block the LEDs and you get no image captured.