Do you have a towbar / trailer socket fitted? Some of these have cut-out contacts to disable the vehicle brake lights (and sometimes reverse lights) when a trailer is connected, so the reflected glare does not affect the driver.

If you have a socket, spray with WD40 and connect/remove a trailer plug a few times to operate the cutout contacts - they may be tarnished ir have a bit of grit trapped in them..

The brake light switch is either faulty or out of adjustment.

Short the wires behind the switch. If the lights work the switch is dead, or may need adjusting towards the pedal.

same question as who is jack!

Do you have 12v out the other side of the switch when it is activated?