You have tons of such cameras, mostly for wildlife record that work on internals batteries (usually 4 to 8 x AA size), internal IR light, trigger on movement record to SDCard then go back to sleep mode until next movement, but you'll have to deal will a few false positive depending the position and field of view.
But if you can power the camera then you have better models than usual wildlife cameras that are IP cams that you will not connect to any network but have SDCard slot.