Why would brake lights quit working and turn signals continue to work when it’s the same bulb?

Might be corrosion on the break light contact. possibly bad wire or loose wire. Maybe even bad contact at the truck plug.

Check fuse panel on the tow vehicle. I have had one go out for whatever reason.

That's a good point. I had that happen one time. It was actually a fuse under the hood that was hard to trace down. I had look in the manual as the other 2 inside the truck were both fine.

Sorry I guess I should have been more clear... it’s a 2006 Ford Expedition it’s towing nothing. It’s my girlfriends vehicle and turn signals work fine, I replaced both bulbs, so I know it’s not them.

If it's on the tow vehicle I would think the brake light switch is bad, or a blown fuse. But it's hard to say with out doing some checks.

The brake light switch is a good start. But I will check fuses too

Sounds like the brake light switch on the top of the brake pedal

+ another. I replaced on 2 Fords

Did your problem get fixed?

Unless the vehicle has amber turn signals, replacing bulbs was a waste of money - the same filament that is the turn slgnal is also the brake filament. If one works and the other doesn't, the problem isn't the filament in the bulb. I don't remember which type that vehicle has. Another hint is that rarely would 2 bulbs decide to fail at the same time. Look for something in common.

Check the brake switch on the pedal stem by removing the wiring connector and jumping the two contacts together (with the vehicle on/running).
Check the owner's manual to see where the brake circuit fuse is located and check that. If it's blown, don't be surprised if it blows again since they blow for a reason.
My bet is on the switch as a failure point.