Third brake light not working properly

Hi, my name is Dan.

It sounds like voltage is possibly backfeeding through the wrong circuit. I've attached a couple wiring diagrams that show both the Center High Mounted Stop Lamp, and the dome/cargo lamp. One thing to check is to make sure the correct bulbs are installed and not installed backwards. I would start by removing all 3 bulbs and then install one at a time to check to see what works.
Use a multimeter or test lamp and check for the correct power and ground at each bulb.

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