Lower brake lights not working

Most likely it is a bad ground. Trace the ground wire for those lights and see how it looks and feels. You can pretty easily reground the wire. If that is not the problem, then the problem is likely in the lead wire. Either way, I believe it is a wiring issue. Here is a guide on checking wiring: https://www.2carpros.com/articles/how-to-check-wiring

Let us know what you find.

Since the tail lights and license plate lights share the same ground with the brake lights, it is unlikely to be the cause. If your truck is equipped with a lamp out warning feature, that is a module inline with the feed to those two lights.