It is actually quite easy using a videofilter with select.This is quite sensitive to video changes:
-vf "select=gt(scene\,0.0098)"
whereas this is not so sensitive:
-vf "select=gt(scene\,0.3)"
EDIT (added your command)
so your command would look like:
ffmpeg -f video4linux2 -s 800x600 -r 15 -i /dev/video1 -maxrate 800k \
-minrate 1k -bt 800k -bufsize 2M -filter \
drawtext='text=%{localtime }:fontfile=/usr/share/fonts/truetype/DejaVuSans-Bold.ttf' \
-vf "select=gt(scene\,0.3)" -shortest -c:v libx264 out.mp4 -y
P.S. You need to explicitly state the codec libx264 and not just tell it -f h264 and why on earth would you be using avi???