Then shop manual diagram is all you have in addition to various threads on this and other forums about this topic. The wiring diagram may seem daunting but if you spend time with it, it will still be daunting but you may see your way to understanding.
Do your turn signals work in the rear? There are many potential failure points for the brake lights and turn signals. The Lucas bullet type connectors are notorious for coming loose, or getting corroded. Often times they are bundled poorly by owners or their mechanics and a bad connection can be a PITA to find and correct. You might first open the trunk and lift the liner to find the wiring harness and locate all the connectors, particularly on the left side if both stop lamps are in op. Be sure the bullet ends are pushed all the way into the connectors. The wires should not come out of the connector sleeve with a gentle pull. My point is be sure they are all pushed in firmly and no wires have broken at the connector. The only other connector for this system is at the flasher relay box I speak of below. It is likley bundled with other connectors right near the relay box.
I'm hoping you are comfortable using a multi meter to at least check for voltage at various points. Since you know where the brake light pressure switch is, first check to see if there is power at one side of the switch. One of the two wires should have 12V when the ignition is on. If you have power at the brake switch, disconnect both wires and jumper them together. If the lights light up, you have a bad switch. If they do not you can probably assume the switch works and your issue is elsewhere. Power for the brake lights comes from the 35 amp fuse on the firewall in the engine bay on the left side. That fuse also powers your wipers, fuel gage, and turn signals. If they work, your fuse is good. If not, check continuity of the fuse and replace if needed.
The ground for the brake lights is through the flasher relay box which is the retangular box, probably with an un painted aluminum cover on the left side of the fender area in the engine bay. They are ugly inside with coils , contacts and what not. Not really repairable but they are replaceable with new solid state units. It has 8 terminals around the periphery which are numbered 1 through 8. Two of them provide a path to ground for the brake lights and the turn signals so that you always have a ground available if a turn signal is being used. Terminal 5 should always be ground for the brake switch. If 5 is not a ground, you likley have a bad relay box. If you can read the wiring diagram you will see the connectors and how the system works.
If you just replaced the brake switch, and your turn signals work, I'd look first at the connectors in the boot. That should be easy. Sometimes all it takes is wiggling some wires with the brake depressed, and press it firmly. These pressure switches aren't like new cars where a slight, light press on the pedal turns on the light. It's a two person job unless you can depress the prake pedal and wedge it to stay on. Three people if one is pushing the pedal, one is wiggling wires at the flasher relay box or at the boot and one is watching the brake lights. If you don't have a ground at terminal 5 on the relay box, a new solid state relay box may be your fix. It is well worth upgrading to the solid state box for reliability. Hope this helps. Let us know what you find.