All three brake lights stopped working at once

In short, no. All three lights don't just burn out at the same time. I suspect you have an issue with the brake light switch. There is an adjustment process so you can try that first. However, if that doesn't work then I would replace it and adjust the new one and see if that restores your brake lights.

I also attached the wiring diagram. If you want to test it, you can unplug the switch and jump the two wires. The brake lights should come on.

Let me know if you have questions. Thanks