It could be the switch, a wiring issue, or the body control module. However, let's check something first. I attached the wiring schematic below for the lights. First, there is a park lamp relay in the under-hood fuse box. Switch it with a different one having the same part number.
Next, there are two fuses I want you to check. Fuse 37 in the fuse box (under hood) is for the taillights. Remove it and see if the lights turn off. If they don't, then we have a short to power after the light switch.
Here is a link you may find helpful:
Let me know what you find. Also, the last pic shows the location of fuse 37 in the fuse box.
See pics below. Note: The wiring schematics were cut in half to make them readable. I did overlap them so you can follow from one to the next.
Images (Click to enlarge)
Friday, November 12th, 2021 AT 5:53 PM