All Rear Lights out on 67 Barracuda

The fuse clips can get crusty and/or loose, causing on/off condition but that wouldn't blow a fuse or disable all lights at once. Brake lamp fuse is hot at all times via one wire going into the fuse box. Turn signals hot only at ign' switch on via a different wire into the fuse box.
I'll suggest that separate issues took all these lights out over a period of time.
First the reverse lamp switch. For 67 model this switch is shifter mounted, low on the column or under the console. Typical culprit.
A separate fault disables park lamps.
A faulty turn signal switch could disable both brake and turn.
Reverse lamps are not as critical so I would postpone that troubleshoot to focus on others. I would pull every bulb and start at the tag lamp. A simple test lamp will check that the brown to be hot with headlight switch pulled to first position. Once it works we know brown wire is good to rear of car. Then check that one of 2 contacts at only rear 2 or all 4 1157 type bulb sockets. I wouldn't run round and round the car yet. All good? If so insert the 2 rear 1157 bulbs. You'll need to poke the bulb socket back into the fixture for its chassis ground. Center the turn signal switch and check brake lamp operation ( a jumper at the pedal mounted brake lamp switch is useful here ). All good? With or without the park lamps turned on? If so move on to rear turn signals. Even with the ign' switch remained off, turn signal switch should work interrupting one or the other brake lamp. so turn ign' switch on to power turn signals. We understand that the flasher wouldn't work while the front bulbs are still removed but the rear bulb and dash indicators should stand on when selected with the turn signal switch. Rear appears to be fine? If so, move on to the front. When you find a "not good" at any of the above, that will lead us toward a fault location.