Strange security light behavior

[Dill Pickle]

So the other day, I start up my 2003 TLC, and the red security light comes on and stays lit while driving, except that when I hit the brake, the security light goes off for the brief period of time that I am hitting the brake. When I remove my foot from the brake, the light comes back on and stays lit until I hit the brake again. Again, this is all occurring while driving. The next day, the behavior of the security light returns to normal, and it has not repeated this since then.

My question is, what is the physical mechanism or pathway for hitting the brake to affect the security light? I do not know enough about the wiring or electronics to answer this question myself.

Thanks in advance,
DP