Park lights stay on?

Hello, you can try unplugging the switch on the steering column that controls the exterior lighting, or go right to the relay that controls the parking lamps and see if its staying latched, the relay is controlled by the Body Control module (BCM). You could pull the relay and see if the control wire(pin) for the relay is staying grounded, meaning the BCM is not deactivating the relay, or if the relay itself is staying latched and keeping the parking lights on. Ill post a wiring diagram that shows the circuit. I assume you're pulling the Park LPS fuse to turn them off?

The first diagram shows the Park LPS PCB Relay which sends power out to the Park and marker lamps when the relay is latched(closed). It is activated by the BCM grounding that White wire highlighted where I've labelled the Relay Control wire. So if you are comfortable testing the wiring with a test light or multimeter, we can have you pull the relay out and see if the control wire might be shorted to ground. With the relay removed there will be 4 pins where it sits in the under-hood fuse box, two of those pins should have battery power at all times, and only one pin will read ground through the Park lamp circuits, the control wire should not read ground with the switch off or the car turned off.
To check for a short to ground and rule out a BCM failure, you would need to unplug the connector at the BCM and check the control wire for continuity to ground. These GM/Chevy BCMs fail quite often. So that white control wire and the relay need to be checked.
You can also check with a multimeter (with the relay out) if the load side pins are still latched closed. They should not be.

If you want to test the relay and the pins where the relay sits, here is what it should read for voltage and resistance, excuse my artwork. But if you are pulling that PARK LPS fuse to turn off the parking lights, then power is coming through the relay, so we would need to check if the body control module is keeping the relay closed or if the relay has just failed itself and is keeping the park lamps powered up.

Here are some guides to help with checking relays, using a multimeter, and using a test light. Testing may sound confusing but its not that bad, we can walk you through it if you have a meter.

https://www.2carpros.com/articles/how-to-check-an-electrical-relay-and-wiring-control-circuit

https://www.2carpros.com/articles/how-to-use-a-voltmeter

https://www.2carpros.com/articles/how-to-use-a-test-light-circuit-tester