My bet is on the bulb out sensor relay. The brake light circuit is often the first one to go in my experience. The bulb out indicator warning light may or may not be lit, in your case it won't be as both sides are affected.

It's often best to diagnose this starting at the bulb sensor relay. Pin 54S is voltage in from the switch. The corresponding point in the socket is a convenient test point to confirm voltage is present when the pedal is depresssed.

Failing that, wrap a jumper around the base of pins 54S, 54R, 54L and S (S is the 3rd brake light). Be careful not to short to neighboring pins, safest to bare only where you do the wrap, which is a bit more tedious. Thin 16G works fine for this, preferably solid core so there are no strand tails accidentally sticking out and less likely to be broken during insulation stripping. Re-install the relay and if the brake lights now work then you'll know that's it. You can continue to drive this way until you're ready to replace the relay or attempt to repair it.

Re-soldering the relay fixes it 90% of the time, one of Art Benstein's favorite repairs. If you want more information there's lots to be found on this site and others. Pay particular attention to re-flowing the solder on all connections for those same pins, esp. pin 54S in our case, following the traces on the lower board to the upper board as needed. Be carefully about moving the sensors that run through the middle of the coils, the ceramic glass coating is brittle.

Second after that will be the brake light switch at the pedal, which you can confirm as above or by measuring at it's connector. These cars are at that age when those switches are starting to wear out. As mentioned by others, diagnosis can be done at the switch connector with a meter, test lamp or even using a jumper wire. If you happened to have cruise control, there would be separate switches at the pedal. The cruise control switch has a vacuum tube on it.
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Dave -still with 940's, prev 740/240/140/120 You'd think I'd have learned by now