How do I change my timezone itself? Not just my location settings or manual time adjust

My Mac won't give me any options outside of Eastern Time. It locks in the timezone setting itself. I need to set my timezone to Central even though I'm not located in a Central Time Zone. How do I do this?

I don't want to manually enter a time in, I just want to change the actual timezone itself.

The "closest city" options is only giving me cities located in EST.