If it is a "LS1" conversion........
Check your grounds!
The headlights are hot all the time thru fusible links
the tail lights are fused power.
Maybe your problem is in the parking light circuit?
They go on with your headlights and it seems to happen when you hit your brakes.
remove the stop / haz fuse, tail fuse and turn - b/u fuse - see if it still happens.
If it doesn't then insert one fuse at a time until the problem reoccurs.
At least then you will know what circuit you have to concentrate on.
You are either grounding out somewhere or a ground is not making good connection and the lights are finding ground through another circuit.
Since the parking and stop lights are a battery circuit, you could be drawing too much amps from a direct short to the battery.
Maybe!
I had a bad bulb in the tail light of a car that when I hit the brakes the parking lights and the dash lights would go on.
It also would make the engine do weird stuff.
It was a bad bulb.
It lit but the glass part of the bulb spun in the brass socket.
Electricity does some weird stuff sometimes!