Back before digital game cameras existed I built one for a digital camera.
It used a weather tight enclosure.
I used RC can servos (that I gutted the servo part and just use two limit switches, one for "home" the other for the "take photo" position, that pushed the button).
It required me to build two timers, the first was the time the button needed to be pressed for the camera to come out of "sleep" mode and take a photo. The other timer was the time inbetween photos.
It took two 6 volt battery's, both would supply 12v dc to the IR sensor and just one provided 6v to the camera. Two AA battery's ran the servo only.
I didn't have anything but time (a lot) in it and it still works better than many digital cameras that are out today.
There are decent digital game cameras out these days that work well and require less knowledge to work, much less built from nothing.
I actually went to game radios shortly after building it, for "active" hunting. As a camera is not a huge step better than just tracks. In other words, you know what WAS there but not that it IS there.