How can I find a cheap battery powered surveillance camera to catch taggers spraypainting a fence?

My elderly neighbor just put up a new fence a few months ago and now it is spraypainted. I know that once she cleans it, it will probably only be spraypainted again. I feel bad because I think she is a widow on a fixed income. I want to help her plus I want to keep taggers out of my neighborhood. I'm thinking a small surveillance cam would do the trick. Any advice? thanks!!!