For a moment I thought maybe you were on to something with checking the canbus line (maybe getting pulled down with module plugged in) but then (one would think) you shouldn't be able to access the module through the bus. You get an "A" for effort though!
I would be checking the vehicle lights even though they "seem" to be fine there could be a bad connection, poor ground, bad (maybe shorted)/wrong bulb that only comes into play with the module plugged in.