1964 Valiant No Brake or Parking Lights
If you don’t have a volt ohm meter (VOM) get one as soon as possible, they are 10 to 25 bucks, and one cannot easily diagnose electrical problems without one, also a test light is real handy to have as well.
I replaced the tail light bulbs with 1157's and now the turn signal lights work
If turn signal lights work, grounding of lamp holder is good. As suggested, check adjustment of brake light switch mounted on the dash side of brake pedal arm. While under dash, also check switch’s continuity, in other words dose electricity pass through it, and will it brake the circuit when depressed.
Parking lights are a separate circuit from brake & turn signal light feed from headlight switch. Consult electrical diagram for your car to help trace it out, and test it. Look here for diagrams: http://www.mymopar.com/index.php?pid=18 Both brake light and parking light circuits run behind the driver’s side kick panel, and along edge of carpet to trunk.
Back up lights are a third circuit switched by gear shift position feed from wiper switch with white wire. I’m not familiar with your year car, but look around end of steering column in engine compartment, or floor shifter if equipped for switch. You will need to make sure that switch is adjusted correctly, lamp holders have a good ground and free of corrosion, and bulb is good for starters.