My 2001 Toyota Corolla will not come out of park without using override on.?

This is an auto trans model. I have replaced the brake light switch on brake peddle and even though issue went away it still reappears intermittently. I seem to have located a solution that involves unplugging a set of wires near the fuse box that will reset problem but it reappears intermittently without ignable cause. Looking for information on what other components are involved in this circuit such as relays or solenoids involved with the brake light switch and gear shift.