Why are the taillights not working?

I would check the fuses # 2 and #3 in the under-hood fuse panel and if they are okay replace the park lamp relay. here is a guide to help you check the fuses and the fuse and relay locations in the diagrams below:

https://www.2carpros.com/articles/how-to-check-a-car-fuse

Check out the diagrams (below). Please let us know what happens.