Hi,

I would definitely check the brake light switch first.
Since you have to go under the the dash and behind the knee bolster to get to the switch you will find the bulb out sensor near there.

The switch itself is a plunger type. It activates by being moved outwards or being released of pressure on it. It can get sticky or corroded on its terminals as there can be moisture of wet shoes from time to time.
Try the terminals first to clean them.
While they are off attach a volt/ohmmeter to the spades and activate the pedal for a continuity check.
You want the switch to be on shortly after the pedal being depress and before the brakes pump up but go off every time so the cruise control will operate.
If it the switch it will not work so I ask do you have a cruise control?

They can stop working by either electrical or a vacuum valve on clutch versions.

I’m not aware of brake lights being grounded through a transmission circuit or a relay being used. So that a new one to me. But it’s plausible and worse with the newer cars and their sophisticated electronic monitoring.
Be happy that this is a somewhat simplistic 245.

The brake bulbs or rear lamps housings should have their own ground returns.
That would be the next possibility in the tailgate third light and could be a hinge problem with the grounds back there.
Since it’s all three you will have say the pedal switch should first and then keep looking if not.
The bulb out sensor only works when there is a current draw difference from the right to left sides of the car.
If there’s no lights at all, the sensor doesn’t see a thing! Consequently no indications.

Hope this helps to open your view to the wiring system, as squinting at those wiring diagrams, takes due diligence.

Phil