No parking lights or tail lights. just headlights

i have no parking lights or tail lights when i turn the head lights on only the headlight is on. brake lights, blinkers and reverse lights work. i jumped the relay socket and they all work. replaced the relay still nothing. i also replaced the headlight switch still have the problem. any suggestions? it’s a 2003 Chevy silverado 2500HD

If you jumped the relay socket and the lights all worked but replacing the relay didn’t fix it, that leaves only 2 possibilities. The new relay is bad or the socket itself is bad.
See if you can find another relay with the same # and swap your new relay for that. If the circuit with the same number relay still works, both relays are good.

Did you check the associated fuses?

The body control module turns on the park lamp relay based on input from the headlight switch. Test for power and ground of the control circuit for the park lamp relay.

If the body control module is faulty, would jumping the relay plug turn on the lights?

Jumping the relay output will prove that circuit but not the relay control circuit. A power and ground on the control circuit is needed to switch on the relay.

Thanks for the information.

Yes, the body control modules is upstream of relay.

Nevada_545 is exactly right. The control side needs power and ground verified as the next step.