I had that problem after getting a viper alarm installed Never did figure it out finally just wired it to the switch and got brake lights I had to turn in my tags last year cause I have no turn signals and just got tags again wonder how long for they catch me again for no inspection.
If you figure it out let me know it has to be something under the dash around the same place as that module your talking about cause if I messed with all the wires in there the would work for a few minutes also you might try the relay thats under the dash it is in a little box like thing looks exactly like the fuel pump relay box under the hood I think it was the blue relay for the turn signal.
I hope this may help I never did find mine. I went as far as putting a new wire harness in the tail lights, new relays, bulbs, stop light switch, took out the $700 alarm, and gave up after hours and hours under the dash.