Any suggestions for battery operated closet lighting?

The ones I use (see above) are actually on a 3' strip. You can stick the strip anywhere you need the lights to shine. The motion detector uses a magnet to attach to a little metal disk you stick on near the strip.

I have these strips in my bedroom closets, a linen closet, and a pantry. The motion detectors have a fairly wide angle, and are usually triggered by simply opening the doors. The bedroom closets have bi-fold doors, and the other two have regular doors.

I also have two more like what @CAZ linked to. One is used to illuminate the floor of one of the bedroom closets, where I keep shoes. The other is used as an under-counter light in my laundry room. The motion detectors on those also work very well. In the laundry room, it often comes on if I just walk past the door. The closet comes on when the door is opened.