I had this same problem on my '78 Bronco, and it ended up being the fuse. It wasn't making good contact, I'm actually running with it 1/2 way pushed in now for it to work
Trying cleaning the contacts (don't know exactly what they are called?) where the fuse goes into.
Agree with everyone. I would first replace all your bulbs. I found that O'Reily's bulbs were about half the price of AutoZone. I think a 2-pack of both the combination blinker/brake light and a 2/pack of the single-prong reverse light were each about $2.99. If that doesn't do the job, break out your multi-meter...