According to my Chiltons drawing, the 87:
Starts at the fusible link which is shared by all the lights that will come on with the key off.
It then goes to Fuse 3 which is shared with the Hazard lights, but not the turn signal.
A pink and black wire goes from there to the Brake pedal switch.
A Lt Blu/Blk wire goes from there to the column harness connector.
A white wire goes from there to the turn signal switch.
The turn signal switch will use, the Hazard input, the brake input or the turn signal input to illuminate the rear bulbs.
Your headlights work so the fusible link is fine.
Your turn signals work, so everything from the turn signal switch in the column to the rear lights should be fine.
Try your Hazards. If they don't work, check Fuse 3.
If your Hazards work, then all that is left is:
(in order of my opinion of probability)
1. the connector on the brake switch could be loose
2. the brake switch is loose and moves away from the pedal, or even fell off
3. the switch itself went bad
4. the wire has been pinched or cut before or after the switch
5. the wiring harness on the column could be loose (this would usually show in other systems also so not as probable unless that wire is the end wire on the connector)