1989 Chevrolet Silverado Parking/Brake Light Issue

I have a 1989 Silverado c/k 1500. Before I press in the parking lights and or head lights to the left of the steering wheel, all is fine. Once I turn either of those lights on, the brake lights no longer function and the rear parking lights do not turn on. So at night, no one can see my tail lights. But the blinkers in the rear still work, and the emergency lights. The front head lights work fine as do the front parking lights. All lights on the dash function properly. I have a trailer hook up and when I hook the trailer up all is fine with it. Its parking lights work, as do the the brakes, when the trucks lights are turned on. They work, while the trucks rear brakes lights and parking lights do not.

The trailer hook up has a ground to the frame under the bed as well. There is also another ground before it is split to the trailer wiring. Both look ok. Two days ago I replaced the rear circuit boards and all lights. Both of the blinkers blink fast and have so since I bought this truck. Even after replacing the circuit boards and lights they blink rapidly. I am not concerned with this, but wonder if there is some relationship there, although as mentioned, they work when the park lights are on.

I am not sure if there was a tail light issue before the trailer hitch was added.

A friend suggested replacing the parking/head light switch, which I did yesterday, to no avail. Any suggestions?