If neither the brake lights OR turn signal lights work, check that your 4-way emergency flashers work.
If they do not, it could still be in the light bulbs, the lamp sockets, the housings are not grounded to the body (the backup lamps have their own separate ground wire however), the wiring between the firewall and the back of the truck (do you have dual exhaust or has some suspension or under-frame work been done recently?), or the turn signal switch in the column.
All of the above are very common ailments with Broncos. Has the Bronco been painted recently?
The turn signal flasher would only effect the turn signals, but would have no effect on the brake lights, or hazards. However both of them could be worn out.
You could also have multiple issues. Well, you do have multiple issues since the backup lamps might be a separate issue in themselves.
Is this an automatic transmission, or manual? If an auto you need to check your wiring right up to the neutral safety switch on the side of the transmission. These fail often too, now that the Broncos are all getting close to that magic number 50 in truck-years.
When did this start? Is this your '76 or something else?
Paul