I took out the light switch and examined everything. It's hooked up correctly but I did notice there is no orange stoplamp wire for the "S" terminal. Though the brake lights do go on when I depress the brake pedal with the headlights off. The "headlight group" on the wiring doesn't have an orange stoplamp wire. Could that be the problem?

The front park lights go on in the park light position, then go off when the headlights are on. The back lights are very bright with the headlights on.