Well, Warlock III was right in saying that I should look at the wiring in the steering column. It seems that that is exactly where the problem was. I believe there is something disconnected or broken in the hazard switch thus the reason there was no power continuing to the turn signal switch. When I ran a jumper wire from the hazard switch to the turn signal switch, the brake lights (with the lights on) began to work again.
I then ran a wire from one switch to the other. Hopefully, this will put an end to my brakelight woes.