The brake light will be on and off?

Hello, does this only happen when you're driving? Not sitting still. It sounds like you may have a lose plug on the back of the combination meter. It's called a pin fit issue. Or the combination meter is going bad. It sounds like the problem is isolated to the gauge unit (combination meter).

Check this guide out

https://www.2carpros.com/articles/brake-lights-not-working

As long as there's no other issues such as check engine light or other lights involved. There might be the longer the problem exists. Its probably the vibration of driving causing the plug to move. As you can see from the diagrams they are both controlled by a micro computer inside the meter.

Yeah, it sounds like a loose connection somewhere or the micro computer is acting up. The combination meter is pretty complicated, there are computer data lines called CAN bus that are connected to other modules in the car. So since the problem is so far isolated to the combination meter, I would start there. The plugs for power and communications are on the back of the meter and need to be checked first. If the tachometer is dropping out too.