Using a multimeter check the contacts as follows:
1. Check for continuity on the tailgate side buttons. You should read very close to 0 ohms on the meter. If you get a high resistance reading, replace the bulb, as it has a bad filament.
2. Check for voltage on the tub contacts. You should read very close to 12V on the contacts when the brake pedal is depressed. If no voltage is present, then you need to dig a little deeper.
It is common for the wires to come loose from the contact buttons , so look under the wheel well liner and make sure that everything is connected and tight. The pins may look like they are connected, but if they are not properly seated, you will not have good contact.
Beyond that, you are going to be looking for wiring issues such as rubs or breaks that have exposed the conductors.
Fuse Position#2 - 20 amp yellow fuse - Stop Lights; but if your Brake lights are working normally, then this won't be the problem.
Good Luck & keep us posted