How can I determine the battery life for a continuously recording camera module?
To answer the question you need to determine for yourself what kind of camera you are going to use, what kind of video resolution to have, frames per second, and what kind of MCU can handle this data stream and put it on a uSD card. 

As a ballpark example, take available options: Raspberry Pi ZERO, and camera module V1. You will probably need a highest capacity uSD card, video class. For a 720P H.264 video you will need about 64 GB for 10 hours of recording. 

According to some sources in Raspberry community, a camera and MCU might consume about 200 mA in continuous 720p mode. A SD card might take anything between 50 mA to 100 mA on writes, see this info. 

So, the target consumption is likely to be about 300 mA. This is substantial.

Now, 300 mA for 10 hours (at 3.7V Li-ION cell) will land you with one high-quality 18650 cell with 3000 mAh capacity, approximately speaking.