Actually your conclusion is incorrect ... the stop lamp switch ( located at the brake pedal lever ) is part of the interlock system... the fuse that would come into play would be 7.5amp # 11 .
With the
key ON and by depressing the brake pedal the stop lamp switch combined with the park position switch completes the circuit to energize the shift lock solenoid.
Here is a description as to how the interlock works

.
The majority of automatic transmissions ( including yours ) have a park gear with a device called a parking pawl which prevents the output shaft from turning ... basically it locks the transmission so the vehicle won't move while in park. While on an incline there is stress on this pawl/gear and it helps to alleviate this by applying the park brake before putting the shift lever into park.
Search the forum as to where and how to download a factory service manual for the Pathfinder... it's free.