Hi,
Since the front parking light turn off and the rear stay on, I don't think it is in the switch itself. It makes me think there is an issue with the tail light relay or a short to power at some point.
Below, I attached the entire wiring schematic for the exterior lighting system. In pic 5, I included the location of the tail light relay. What I want you to do is locate that relay. Remove it and switch it with another having the same part number in the box. Do the tail lights stay off with the new relay? If so, replace the relay. If the lights stay on with the relay removed or with the new relay, we have a short to power.
If there isn't a relay having the same part number. here is a link explaining how to test one:
https://www.2carpros.com/articles/how-to-check-an-electrical-relay-and-wiring-control-circuit
Let me know what you find or if you have other questions.
Take care,
Joe
See pics below.
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Sunday, May 9th, 2021 AT 9:00 PM